That's most anti-cheats, not just Epic's. BattleEye has taken it a step further and even blocked virtual machines. Even Valve's own VAC has issues with Proton: https://github.com/ValveSoftware/Proton/issues/3225
Seems to be speculation and anecdata but thanks for the link all the same, wouldn't surprise me if it turned out to be true. Disappointing. Haven't played multiplayer in a few weeks so I could be in for an unpleasant surprise next time...
The anti cheat R6 using is Battleye instead of EAC.
And the reason anticheat did not works with wine is mostly because they use kernel modules, which you obviously can't run a windows kernel module on linux kernel.
If you run it in a VM, most of them will just fine with it.
Unfortunately Epic is notoriously Anti-Linux, from their CEO down. So the status of EAC under Linux is a giant question mark