From my understanding, if you play an EAC game on Linux with Proton, you're not really running the same EAC as Windows players. You're running a lite version that runs as a regular user and it tries to provide at least some level of protection like verifying game files or detecting anything clearly out of place that it can detect, but obviously it doesn't have the permissions to see everything running on your system or install a kernel module. This does mean cheaters could probably just cheat on Linux to bypass it more easily, so anticheats like EAC will put Linux support as an opt-in toggle which some developers choose not to enable.