Earlier quoted context omitted.
Forgive my ignorance, but why do game servers ban Linux players in pvp games? Fear of some sort of modding only available on Linux?
Modern anticheats are basically kernel rootkits which go even to the point of trying to checksum your drivers and inspect how they work. They're basically as invasive as they get. They obviously can't hook into Linux kernel so they react by just banning the player.
Something that I find interesting is that anti-cheats are needed when either 1) the input can be somehow enhanced (think fps aim hacks) or 2) more information than the player should have is being sent to client (think fog of war or wall hacks). That's hard to avoid in shooters, where you need that behind-the-scenes information to reduce perceived latency. But games that don't have that low-latency-hungry "twitch" element, like strategy games, turn-based, etc., can make do without information that would enable hacking (and they usually don't benefit from input hacking either). I'm currently working on a pvp strategy game that uses an exaggerated input delay as a game mechanic, which also gets rid of the need to send information that the player shouldn't have: ground-truth is computed server-side and after pruning and transforming according to each player's perception, streamed to the clients. That's unhackable in the game hacking sense.