The post on the Lutris forum, has multiple people claiming the same thing. This wouldn't be the first time playing an online game with some form of Wine got people banned, as the same happened with Activision Blizzard and the game Overwatch although the majority of those bans were overturned. In this case, things might not go so well with EA already telling users they will not "remove this sanction from your account"—ouch.
Just another reason why I continue to fight for supported Linux releases. Support developers with your money that support the platform. Playing with Wine (and so Steam Play Proton too), is almost always not supported by the original developer and so they have no reason to actually do anything when problems like this arise. As much as it's a terrible situation, it's best to not play multiplayer titles (EA especially it seems) with Wine based solutions if they have anti-cheat systems in place.