I am wondering, whether what I read online makes much sense in regards to exchanges "banning" mixing services.
I tried it and it seems not. I have tried to mix very small amounts through various mixers and used an account on a major exchange to see wheter they will have a problem with it (as they claim) or not.
Fact is no issues after weeks.
I guess you mean Binance when saying major exchange because it has the highest volume. I would say that you never know what kind of funds you receive when someone sends you the money. Imagine, someone pays me $100 for something, why will I know that it's from mixer? When someone pays $100 cash, how do I know that exclusively that banknote was used for crime, murder, etc? You are only under "radar" when you do something bad. If you do something bad, then don't count weeks, you may get caught at any time.
Otherwise, don't worry. I have received mixed money on Binance years ago without any problems and don't even think that it will cause problems for me in future.