I had some contact with battle.net support when an Overwatch ban wave hit many, though apparently not all, Linux users. I filed a ban appeal, where I also mentioned that Blizzard has stated that compatibility layers (e.g. Wine/Proton) does not violate their ToS, and that Blizzard has previously reverted accidental bans of Linux users. The support tech replied that they had checked the system and that our accounts were sanctioned correctly.

I contacted them again, explaining that Wine can look like a cheat to an automatic system, but does not provide the player with any kind of advantage in the game, and reminded them that this has happened before and that it has affected a large number of Linux users. I also asked them to escalate the issue to the people working with the anti-cheat engine. Their reply was along the lines of "I understand that this is frustrating for you, but I double checked and the bans were correct".

At the same time I was talking to other Linux users who had the same thing happen to their account, and they all got similar responses from Blizzard's support. It looked like the replies were written by humans, but they were not helpful in any way.

2 or 3 days later we all got an email from Blizzard with an apology and our accounts were reinstated. So somehow this issue probably made its way to people who actually work with the anti-cheat, and have the power to do anything about incorrect bans. But I seriously doubt the people answering my emails did anything at all.