I don't think they can do that against JoinMarket. But they could blacklist addresses that receive mixed coins (CoinJoin tx are very recognizable).

However, CoinSwap is being developed. This would be a way to unnoticeably swap your coins on-chain. CoinSwap tx would look just like regular tx.

I think we can use Lightning to escape the blacklist of on-chain addresses. We can open a chanel and send btc through lightning or send on-chain btc to muun wallet and send out through lightning. Since the lightning receiver will not know the origin of the btc so the blacklist will not work.

send out through lightning

In this case the provider will refuse to do submarine swap.