It is entirely possible to trade peer to peer without giving away any personal details whatsoever. You just have to be considerate of the fiat payment method you are using and the other party you are choosing to trade with. Some will ask for ID verification for their own reasons. If you don't want to provide that, then just don't trade with these people.
You are totally correct, but I am specifically commenting about Binance. Some people do say Binance do not require verification unless certain high amount is doposited and wanted to be withdrawn. But, I see this correct if binance user are just sending in and out cryptocurrencies, but not true while trading fiat, including the p2p on Binance platform.
I do not have to say anything about using credit card as it is a form of privacy depriving method of buying bitcoin, but p2p on Binance require users to snap himself, if he did not snap himself which is the fully verified level, he will not be able to make use of p2p on Binance platform. Although, the level for ID verification is not necessary.
So, I was just trying to make more points how Binance does require KYC while people are commenting like it does not require much verification which is completely wrong.