What do you mean by exchange ban them? Does the exchange site be able to detect if the Bitcoin came from mixers? I think it depends on the exchange whether they have on their terms and condition whether they ban those coins or not.
Some mixers or services exhibits certain identifiable behavior and it would be fairly easy to flag them as a suspicious transaction, CoinJoin namely would have many inputs and outputs with some of the outputs having consistent value. It is not difficult for them to identify it but tracing it would be a problem.
Transferring the coins a few times after mixing could probably solve the issue. This way, there is an argument to be made that you're not the one using a mixer and instead the person who sent you the coins did. It's not a guaranteed success but it would be better than sending the CoinJoin to them directly. Keep in mind if that if an exchange doesn't want you to use CoinJoin or any mixers, then your privacy is under threat anyways. I consider them complicit with helping the government to track their customers.