Using Cloudflare for anything risky seems short-sighted, but rather than just complaining about that, here is a proposed solution: https://njal.la/ (not affiliated, just a grateful user)

100% focused on privacy, relatively cheap, available over Tor, established by Peter Sunde (of ThePirateBay/IPredator/Piratbyrån fame) and finally in 2020 RIAA and MPA both complained about Njalla which gives a bit more confidence Njalla haven't completely sold out yet.

I don't think I'd even go for a mainstream US service like AWS, Google or Cloudflare if I what I want to host is even slightly controversial-but-not-illegal or where I prefer the hosting provider not to know who I am.

(worth noting though, Njalla is still a company who has to follow the applicable laws, so unsure how much it would have helped in OPs case)