There is no exchange todah that doesn't asks your data. Your government will ban the exchanges operating illegally in your country if they don't cooperate with the government and comply to their laws. You can be assure that it doesn't just stop to compliance and cooperarion when it comes to tracking funds.
I sometimes trade on the Yobit exchange and verification has never been required there. Earlier, I made a topic on another forum in which I wrote about many exchanges and most of them did not require mandatory verification. If you don’t only look at the top 10 exchanges, there are a lot of such exchanges, you just weren’t looking.
I like yobit alao but I'm not sure if how big must the BTC you deposit before they will ask our data. I have tried them before and although I personally didn't experience issues with them, I just don't know when it will happen.
The accusations against them are probably just accusations. People echo what was accussed that even the new crypto users avoid them.
Withdrawing BTC from the yobit exchange means BTC can only be traced it from them and the exchange serves as mixer?
Any exchange can serve as a mixer, even those that require account verification, which is very easy to buy now, those who need to pass cryptocurrency through a mixer will buy verifications on exchanges or simply use regular mixers.
If we are not talking about the fact that exchanges without verification can be conditionally considered mixers (which is stupid and completely wrong), then even if someone is forced in the future to have mandatory verification, you will be allowed to withdraw money without it, this practice was on all exchanges.
But if you are afraid of this, then use decentralized wallets and exchanges.