I'm a member of TST, but I have issues with them as well; so while I am about to post here defending and supporting their better aspects, please understand that I know they have faults too. One of the fundamental aspects of Satanism is individual self determination, so it would REALLY be anti-Satanic to just toe the party line.
The first thing to get out of the way is that of course any dogmatic follower of LaVey will deny the legitimacy of any other faction claiming to be Satanic. That accounts for a large percentage (maybe half) of posts I've seen claiming TST is bogus. See again about toeing the party line.
TST was started first as a humorous fiction, for a student film. When the pranksters realized their idea of Satanist political action toward church-state separation had merit as something to do "for real", they did it. They realized that their position in court would be bolstered by legitimizing their identity as a faction of an already-established religion, so they did everything necessary to assert themselves as "real religious Satanists", just as other Satanic groups have done before.
In the process they gained a lot of new members, especially people attracted to the progressive social justice aspect, and lost the ones who were more interested in the 1960s/70s vision of what Satanism should be. I don't have any data on actual membership or growth/decline in any of these groups, but the public outreach events and campaigns of TST are obviously more likely to draw followers than the more passive and exclusive approach of older groups. It is "trendy" because it appeals to the current zeitgeist.
The world is changing rapidly. Early Satanism reacted to the stifling oppression and squareness of the 1950s and early 60s by advocating hedonism and specifically anti-Christian ritual, and it reacted to the brainless abandon of the hippies by rejecting "trendy" socialism, turning toward isolationism. TST, representing modern urges, reacts to oppression with legal challenges and a broad rejection of dogmatic thinking and selfishness. In the earlier days it was rebellious to say "I don't care about any of you, I'll do what I wilt"; today it is rebellious to say "I care about all of you, and I will defend your freedom in court".
Personally I define Satanism as conscious rebellion against oppression, especially from theocracy. I align with TST because they are doing much, much more to actively push back against the oppressors than any other Satanic group. The others may be more deeply devotional, they may be more arcane, they may be more "evil" or more Randian in their individualism, but they make no effort to do anything to overturn the oppressive system. Hedonistic rituals do exactly as much good as prayer--that is, none whatesoever, unless the ritual is a means for engaging people in efforts that might actually achieve a victory.
Some old-style Satanists will assert that individual victories, by imposing their will on others, is proof of the effectiveness or validity of their version of the faith. But you can only have such a victory by being stronger, while the other party is weaker. How is that a rebellion against oppression? Frankly it IS oppression. At a minimum, it does absolutely nothing in the war against theocracy (or against God, for the theistic).
Remember that LaVey was always quite open about his view that religion is a scam, and that religionists are carnival hucksters. It's not hard to imagine that he wrote the "rules" of Satanism much the way Hubbard wrote Scientology: to prove a point, and to establish himself as the source and the head of the faith, for a life-long career. Those with open eyes can see that the books and teachings were an overt act of hucksterism, with a knowing wink to those who got the irony. So how could it be wrong for a different group to write their own version, serving a new purpose, especially when that new purpose is explicitly for the greater benefit of all people through the separation of church and state?
Critics say TST is mainly a progressive humanist group, so they shouldn't use Satanism as their assumed identity. But if you look at the initial aim of the group, to block Christian symbols from being erected on public/government property, what else could they have done? They had to use existing laws preventing religious discrimination, and in order to effectively do that they had to represent a religion that would be discriminated against. In order to get the desired result, they had to be a religion that the Christians could not tolerate. They could have assumed an Islamic identity toward that end, but state Islam is fraught with problems of interference in private life, in its state-sponsored form making an equally bad (if not worse) example of the issue they wanted to address. Really, it had to be Satan. Now that they have had regular successes in this field, it only makes sense to build on this identity even further. In this way, they are exactly following the established tactic of LaVey.
My goal is to use TST as a tool for leveraging progressive social values and fighting back against theocracy, and I'll exert my voice and actions to shape that tool. Already members have shown broad support for TST's work in court, and have pushed back critically against some of Blackmore's words and actions that don't help the cause, and membership seems to be growing. This actually demonstrates the validity of TST as a creature with its own life, "real" as a sort of religion, and "real" as a form of Satanism, simply by virtue of its healthy growth, regardless of whether it suits people who have their own ideas about what it should look like.
The door is always open for members of other Satanic philosophies to work together with TST, or change it from within, if you want to use your faith for the public good. If you just want it to be about self empowerment and dominance, you don't need the term "Satanism" either; you could follow Tony Robbins for the same result. If you theistically believe in a real Satan or Lucifer or other demon beings, that's your right of course, and I believe TST's public actions do not detract from, or defame, any Satan you hold holy, so there should be no problem coexisting. Their secular work might even be a great benefit to your religious faith and life.