you're not getting banned from steam, you're generally getting banned from participating in anti cheat secured lobbies of a single game or a group of games.
single player experience is generally not affected.
having a 3 strike system before getting banned from multiplayer just means it's 66% cheaper for a cheater to get a new copy of the game.
this is also not new and has been the case for the current family sharing system as well.
it doesn't seem to be server specific because once prompted there is no way to use the account again, even if you decided to just not use a server that may have these settings set.