Greaves grifts off of the brand and makes money through the IP. Many of the lawsuits they file are poorly done and interfere with other efforts to safeguard reproductive rights. The leadership discriminates against LGBTQ members and actively attacks anyone that speaks out. This is because Lucien is a fascist with a history of saying nazi things with white supremacist criminals.

This video by Dead Domain, an enby who infiltrated a hate church and CPAC, explains the situation and links to a document with more info.

I suggest you read about QueerSatanic. TST is known to sue anyone who criticize them. So much for the freedom to offend, I guess.
About the separation of church and state, they haven't achieved anything. What they fought for is not secularism, but plurality of religion, which is just as bad as nothing - they actually pushed for more religious symbols in public space, instead of fewer. About reproductive rights, or their activism in general, some people fear that they might be causing a second satanic panic, which can only end poorly for satanists all around the world, and give fuel for christian to think that abortion leads to hell.
And as a religion, you can realize that lot of things TST does is un-satanic to begin with; they are martyring themselves and proselytizing. At some point, they are doing the exact same thing they denounce from the christians in the US, like fiscal advantages for churchs and reaching children through an after school program.
If you want a simpler reason to not like them, just know that as a non profit organization, they are not sharing their finance records, which is usually a big red flag. If you want to give to a non-profit, you should at least know where your money is going. Plus, some local branches of TST are actually disaffiliating from the main organization because they don't like how it's managed. Finally, there are already organizations that are fighting for everything TST claims to stand for, without the religious cosplay and all the shit around them.