Monero transactions are not traceable. If someone send you monero, it can not be known that it is from a blacklisted address. As you convert it back to bitcoin, more suspicions are also blocked.
I do not talk about this, but within the Bitcoin blockchain, no changes happen. If my address was on the blacklist and I used the BTC XMR exchange, what happened is that my bitcoin were transferred from my address to another address. It has not been mixed, and if the other person deposits it to CEX, it will be frozen because bitcoins are still blacklisted and can be tracked.
In the case of mixers, it is transferred through thousands of intermediary transactions, which means it is difficult to trace its blacklisted origin.
This can happen to you even if you are using normal mixer that is using BTC to BTC mixing, without any use of monero or other coins.
This is not true. When you mix your coins you will obtain them from many sources and thus you break its link with their blacklisted origin.
If we assume that what you are saying is correct, then before using the mixer your coins would have been 100% frozen, but after use there is a possibility that they will be frozen and a possibility that they will be accepted.
You'll encounter most of the challenges listed here even if you use a mixer. Swapping BTC to xmr and back to BTC provides a high level of privacy if you do everything correctly. Blacklisting addresses is one of the ways the government attacks BTC's fungibility and it is mostly people who use centralized exchanges and custodial services that are at risk of their funds being confiscated.
You did not understand what I am trying to say. It is true that you, as a user, broke the link between your old and new transactions, but the old transaction is still blacklisted and without mixing it you moved this problem from you to someone else.