Thank you so much for info about this. Does anyone has list of known "traps" like that on Cloudflare? I only want to use them for proxying my IPv6 website, SSL, and nothing else.

Cloudflare used to effectively allow you to block users coming from Tor or proxies, forcing them to chose between not visiting your site or disabling their privacy features. (when Akamai was able to still allow legitimate users)

They do a much better job these days, at least

There are countless objections to many of the things the Cloudflare is doing. If you only need it for a small number of things perhaps it may be worthwhile to look if at whether there are alternatives to CF for those use cases.