Anti cheat software tries to find cheats running on the computer, and in order to that, so called kernel-level anticheat hooks into NT (Windows kernel) internals, and runs at the highest possible privilege level. It has to do that so it can monitor everything going on in the system. If it didn’t do that, the cheat could just hide from the anticheat software by running with superior privileges.
Wine does not implement undocumented/internal parts of NT, and neither does it run at an elevated privilege level. It also cannot realistically implement any and all possible NT kernel internals, and it cannot possibly hide the fact that it’s actually wine, and not real Windows, from any program that really wants to figure this out.
If wine tried to implement a specific workaround for a specific anti-cheat software/version, in order to it trick into thinking it’s running on a real Windows system with elevated privileges, the anti-cheat vendor would likely interpret this as a kind of deception, and they could easily update their software to detect this situation.
Theoretically, anti-cheat vendors could do kernel-level anticheat for the Linux kernel specifically if the game runs on Linux, but this has problems: First of all a general backlash and complete lack of cooperation from the Linux community (btw, Microsoft isn’t too happy about them doing this on Windows either, and they might at some point do something about this, since it’s bad for security and stability). Also, Linux kernel internals aren’t at all stable, and so just practically you cannot hook into the Linux kernel nearly as easily as you can into NT.
Some anti-cheat vendors do support Linux though, but only optionally if the game dev allows that. In practice, this just means many checks will just be disabled on Linux, which is presumably why many games do not enable the Linux support.
tl;dr: No. Only the anti-cheat vendor / game dev can realistically fix the situation, and they may not want to because it’ll be worse at actually detecting cheats on Linux in practice.
You cannot realistically make it impossible to detect that you’re running on wine. Wine just implements the Windows ABIs. The actual code running is totally different. Even just reading any of the binary code of literally any function would reveal it’s different from the Windows code. How are you going to stop it from doing memory reads on stuff that it needs to be able to read? You can’t. You’d need a full hardware emulator for that.