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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.
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send out through lightning
In this case the provider will refuse to do submarine swap.
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