Valve tries to make it easy to run a proton-compatible anti-cheat system which I believe is built in to steam libraries, but developers still have to choose to use it notably Microsoft seemed totally uninterested in using a proton compatible EAC for Halo Master Chief Collection last time I checked earlier this year. I read online it should have been easy to switch to the proton compatible EAC but some devs might not want to.
It seems to be up to the developer, as many anti-cheat support Linux if the developer wants it to.
Elden Ring uses Easy Anticheat which works fine in Proton, but Black Desert also uses EAC and it doesn't. Phantasy Star Online 2 works with Proton-GE and it used GameGuard and now Uncheater.