One solution to maintain Linux compatibility with good protections could be similar to what Embark Studios is doing with their games (The Finals, and Arc Raiders): Windows version gets Kernel-level anti-cheat and additional layers, Proton branch gets a user-level version of the anticheat instead.

Personally, I would argue that the majority of individual cheaters (who are seeking to undermine their opponents and win with minimal effort) are likely to be on Windows platforms where kernel-level protections would be most effective in detection. With an Embark-style dual solution - you can both catch the most cheaters and score W's with the Linux community.