No, just have the anti-cheat trust kernels signed by the major Linux vendors and use secure boot with remote attestation. Remote attestation can't be fooled from kernel space, that's the entire point of the technology.
That way you could use an official kernel from Fedora, Ubuntu, Debian, Arch etc. A custom one wouldn't be supported but that's significantly better than blocking things universally.
You can't implement remote attestation without a full chain of exploits (from the perspective of the user). Remote attestation works on Android because there is dedicated hardware to directly establish communication with Google's servers that runs independent (as a backchannel). There is no such hardware in PCs. Software based attestation is easily fooled on previous Android/Linux.