You can check the list on Bestchange.com but do not completely trust their information because it's not always updated, so, when you see an exchange that doesn't require KYC, check that manually on the website. There are some exchanges that have KYC requirement but rarely ask. Lots of instant exchanges do not ask for KYC when you send small amount of money.
I am going to go out on a limb and say that 8 or perhaps 9/10 exchanges advertised on Bestchange have KYC as a possibility and/or requirement in their terms of service and privacy policies regardless of what they claim. As soon as KYC and AML is mentioned and you are dealing with third parties that facilitate the exchange of funds, be sure that problems and frozen funds can happen for x reasons. If that is the case, then they can't compete with the service that eXch has been offering for years.
However, if you trade through DEXs, you always have to count on someone seeing your bank details, even if it's just the person you're trading with.
Sure, and that's normal. If I am selling my BTC to you and you are paying with fiat, you'll have to know my personal details, which could involve real name, email associated with the payment service, or bank account information. It becomes more dangerous when such information is centralized in one database, even if it's encrypted, anonymized, etc. We know from past incidents how valuable such information is and that it can leak and be hacked because scammers want to get hold of it.