If such pressure does happen and if it has strong grounds, I think we will see a big fight maybe even bigger than during Bitcoin Cash troubles. Somehow I am sure that Bitcoin maxis will win once again.

The question here is the side the "Bitcoin maxis" will take in this conflict.
If this happens, this will probably be several years ahead (perhaps in the early 2030s). So it's possible that until then, many cypherpunks which also were Bitcoin OGs will sell their BTC once they aren't comfortable anymore with the increasing institutional involvement, if bullish conditions continue this would mean they anyway would have become very rich. They could then become less interested in being involved with Bitcoin, post their opinions and work as "influencers" in the BItcoin community. And that could change Bitcoin's demographics: more "get rich" people, less "ideologically driven" cypherpunks.
And that's the scenario I'd be most fearing: that this FATF cartel is discovered, some remaining cypherpunks may be rising their voice, but nobody of the new generation of "Bitcoin maxis" cares. Because moon is more important ...
For this reason, I think it's important to always remind new users about Bitcoin's essential features like censorship resistance. If that happens and the "new generations" of Bitcoin users become a bit more cypherpunk-ey again, then the privacy side could win in this conflict even against a big FATF cartel. If not, then Bitcoin could become a simple normal financial asset ... and probably will eventually collapse because it would lack its core features.