It's going to be a very long road, but Valve has definitely been working on it. Through a combination of Kernel patches and WINE magick, they seem to have something cooking up. It's anyone's guess as to how effective (or accepted) it will be.
from the mouth of Sauron itself:
> Tim Sweeney @TimSweeneyEpic > Jul 15, 2019 > EAC has native Linux binaries in beta, supporting several native games in active release. This missing link is native Linux anti-cheat integration with Wine/Proton so that games running under Wine are protected. This is in the works but is a big task.