I think what we are seeing in anime fandom is only coincidentally a shift from the specific to the general. I see two possibilities, both of which I think are related and both require understanding anime fans as media consumers.
The first possibility: What is happening is a community and industry shift from "Early Adopters" to "Mainline Consumers"(at least in the United States) .
Early adopters often cling together and to a specific product, and even retain this identity for a long time despite competing products. But why specifically the one product? Well, first of all, because there simply aren't many options. Second, early products, if there are multiple on the market, are all trying to differentiate themselves from each other in what they have to offer. The early adopters thus cling to one product because they know it, and the other products are somewhat foreign, or lack some aspect which drew the adopters to the product they are favor and are more familiar with.
Besides, when something is new (be it anime or technology or anything else) it's difficult enough to change your life and thinking for the one product, let alone all of them, especially since the adopter and the world around them are not used to the new product or idea yet.
So, let's consider the anime community in the United States. When I think back to my childhood and some of my teenage years, I don't recall very many options for anime. If you were growing up at that time and wanted to watch anime, you could watch some very early morning shows, or you could watch Toonami if you had cable TV (which was less common then than now). Of those options, you had, for the most part: Dragon Ball Z, Sailor Moon and Gundam Wing. If you look a bit further back, and were an early riser, you could add Dragon Ball, Speed Racer and Ronin Warriors. These, at least for a while, were all the options I had and can remember.
Look at those options! A super-fighter anime (and possibly it's less serious but charming predecessor), a magical girl anime, a mecha anime, a male sentai anime, and a racing action anime. Few options, and pretty distinct in many ways other than all being somewhat action and battle oriented (likely this similarity was chosen on purpose, because those bringing anime to the United States couldn't take too many risks when choosing their different products and so had to have some common element that had proven successful). Most of these were also long run anime, so they could keep us busy on their own for a long time, and thus we didn't need to try too hard to find something else.
Around this time Pokemon made its way to the network channels for kids, followed by Digimon on a competing network, both fueled by and fueling the popularity of their respective games. Again, very similar action anime with similar business goals, though these were in competition with each other and on separate networks. These are the first anime I remember making their way into the strictly-for-young-children Saturday morning cartoon show slots, and they remained the select few for some time.
Alright, so eventually things open up, and we get Midnight Run and Adult Swim, Toonami gets some new anime, and so on. Then what do we have exposure to? Yu Yu Hakusho, InuYasha, Tenchi Muyo. Maybe another Gundam, a few others perhaps.
So, we're starting to branch out more, though everything is still pretty action oriented. What is important to note, though, was that these series COULD start expanding their exposure and taking up more time slots, and that they started getting wider target audiences (as noted especially with the Pokemon-Digimon case). Keep in mind, at this point the only way most people can get access to anime is through TV broadcast. If you have money, you might be able to go to some store somewhere and find some VHS-only anime, but it'll be kind of difficult to know what you're getting. Most stores aren't going to risk carrying random, unproven products, especially since at this point the target market, while growing, is still relatively small and young.
Alright, so lets fast forward.
What do we have now? Entire networks dedicated to not just anime, but to ONE COMPANY'S anime lineup (yea, Funimation channel might be going out, but its still pretty recent). Several different anime series appeared and cycled through Adult Swim and other areas of Cartoon Network. Sci-fi channel broadcasts anime. Saturday Morning cartoons comprise of a lot of anime. American Cartoons have completed full, successful series in anime-inspired styles.
But TV, even with cable and satellite, are not the only sources of anime. Go to any video store and there are entire aisles for anime, sometimes rivaling the rest of the video selection. The Internet has allowed people to download all kinds of random anime, giving exposure to shows that haven't even hit the U.S. markets, while people can discuss and share what they find everywhere. Funimation now has a streaming service for all their anime where you pay one low rate a month and get as much as you want, much like Netflix, Amazon Prime, Hulu and other streaming services have large anime collections for on demand viewing. There are now many more conventions from which to draw even more exposure, and they get bigger and bigger, simply because there are more people interested. You don't see only action- now you see drama, slice of life, comedy, philosophical, horror, and every other genre you can think of. Why? Because the market is bigger, much bigger, and has been around longer.
That means, by definition, a lot of people have come into this market later in the game, after it expanded. You are no longer dealing with early adopters, you are dealing with a mature market of mainline consumers. While there is greater diversity in one sense, not EVERYTHING needs to be so different anymore. The newest anime can be a re-hash of some other successful show in the same genre (much like we see with American Primetime TV and movies). There's enough of a market to absorb it all.
This also means the market is able to spit out, and consume, much of the same thing over and over again. So, what used to be available only in one show, and what attracted many to that same show, can now be found in 30 shows. And those 30 shows sometimes have aspects which overlap with some other group of shows, which the consumer finds they like because of the overlap. So the consumer begins watching that other genre as well, opening up each consumer to more and more possibilities.
And these new consumers can get all of the new options at will without much effort, and get them advertised, and reviewed, everywhere they go (well, not quite everywhere...yet). Sure, some of the early adopters still like to cling to their old ways of identifying with just one product, but that's just what they're used to. There are new anime, both bigger and smaller in popularity, length or budget, that attract more attention than earlier series, and ones that attract stronger exclusive identification, but as Charles said in his earlier post, the connection is not as strong or lasting as it was for earlier anime fans.
We see this shift happen with other industries. In technology circles this is very apparent. We may think there are fanatics for operating systems now, but in many ways the fanaticism is weak in comparison with what it was in the 80s with the earliest personal computers and Operating Systems. Even in the 90s if you look at just the early GNU/Linux community, the identification with just one of the several distributions of this new line of operating systems was somewhat incredible for a community that favored as core principals the ability to customize and transition between systems at will. Much of the old biases remain today for those that held them for so long. Even something as simple (and obscure to many) as a preference in Command Line Interface or text editors used to bring about heated debates with die hard fans that still haven't changed despite advances in the field or obsolescence for certain tasks.
The second possibility of what we see happening in the anime community is related to the first, but from a different angle. What people sought in their identification with a particular anime, what drew them in, was not the anime itself per se, but something else in the anime, some quality of the medium, something perhaps more abstract. As was said above, in the beginning there were only so many options, and those options made distinctions from each other, lest they become too bland in light of each other and in order to gain larger appeal of the emerging anime market.
Later on this market opened up, and more consumers flooded in, which allowed for an expansion of content that had some aspects similar to each other, sometimes a lot of aspects similar to each other, and brought in some new aspects as well.
Suddenly, those who were attracted to that one quality in an anime, that quality which allowed them to identify with the anime so strongly, were then able to find the qualities in 100 different places. Not only that, but new anime with both the same qualities and new qualities that draw in a new crowd are being produced and released to these fans at a much more rapid rate than had previously been seen. So, what do they do?
Well, since they were attracted to the quality, not the specific anime per se, they go where they find that quality. Now it's in many places, so they go to many places. Before they could only identify with one anime, now they find they identify with many. Before that one anime was the only thing like it for years, now a new anime like the favored anime comes out every year perhaps, or more often.
Sometimes, an anime comes along which strikes a chord, and harmonizes with the qualities the fan seeks stronger than others. Thus, this anime leads the fan, and others, to cling to it stronger, or longer than to other anime. However, the fans don't always feel the need to abandon all other anime that struck similar, though weaker, notes (some do abandon other possibilities and create arbitrary rivalries still, but that's another discussion).
In other words, the fans (or the consumers) are no more or less specific than before in what they are really seeking. Before they sought this one quality, which was present in one place. Now they find it elsewhere, and that is still what they seek. Now, there are also more seekers seeking more qualities, so the community as a whole looks less focused, but that's simply a matter of wider appeal and more to offer to different people. As mentioned above, there used to be fewer genres available to most the public in the United States.
Before, the people were the prospectors looking for gold that found that one small bit and clung to it with joy. Now they, and others, have found the vein, and so they dig in with fervor to the larger amount. The only thing that has changed is the availability and amount of what they seek, not what they seek.
Sure, some of the ones that were there early might hold on to that first nugget with nostalgia and sentimental feeling, because it was all they had for a time, and some may not. Likewise, the new diggers never knew a time where there wasn't the whole vein, and so have no reason to cling to just a small nugget when there is much more to be had. If the mountain is later found to contain platinum, silver and diamond, everyone will find miners of these other materials in the mix as well, that may or may not have a smaller interest in the gold, but do share an interest in precious metals or gems that are offered by the mountain at least.
Of course, where the individual finds this quality they seek doesn't have to be just anime. It could be in manga, video games, art, music, cosplay or any other medium. It could even be simply in the community. Thus, we do see a plethora of media at anime conventions and among anime crowds in general, and the presence of many of these other media continue to expand. This is because these other media share some quality with anime which people in the community seek, and they just continue to look for that quality even as it drifts further from anime.
We see this shift into other media especially with the growing presence of non-anime related music at conventions. There are many who have always been attracted to music in anime, but perhaps they were attracted only to the music in one anime at first. Perhaps then another anime came along that also attracted them to the music, and then another, until the person learns to seek out that type of music. Then maybe a video game had that music, or maybe they discovered a band that does that music. Then the person maybe became interested in making that kind of music and hearing more. Since this happens to more than one person, perhaps panels just on music in anime, then on music from Japan, then on certain kinds of music in general start appearing at conventions. Before you know it, cons have concerts by bands that have never been in an anime, record labels have panels, and dealer booths to show off the latest bands, and there are even entire conventions dedicated to music in an anime convention style filled to a great extent with the same people as attend the anime conventions.
More could be said along the lines described above, but I leave you with one last consideration: I heard about a study a few years ago that found that those who read only one book a year overwhelmingly tend to read the books that are "#1 Bestsellers", and they likewise make up the largest chunk of people who buy said bestseller. On the other hand, all other books tend to be read primarily by people who read many books a year. In other words, the most popular works are popular among, and due to, those who are least involved, and interested, in literature. The less popular works are read by those who are the most interested in literature and have the most general, widest, and deepest exposure to literature, and thus also more points of comparison. This latter group is also far more likely to go to any kind of literary event or convention. I don't know how true this finding is, and I can't find the study that published this anymore for more detailed information and critical analysis (for all I know it's an urban legend of a study) but I still find it an interesting concept.
Does something like this play into what is happening in the anime world? Are those who are most vested in anime watching the most different kinds of anime, though not necessarily the most popular anime, and are they most likely to show up at conventions? I don't know to be honest. Others would probably have better insight into that matter.