P2P is a network that should only comprises of the seller and the buyer to make a transaction, we have a list of reputable members of this forum you can also trust and send them your fiat to credit you with the alsame proportion in bitcoin.
escrow service providers
https://bitcointalk.org/index.php?topic=5047302.0Even in P2P, you would still have to pay through a bank account or something. Or any e-wallet that most likely have your identity but at least you have more freedom in the method you can use to pay and there is only one person that you have to transact with as opposed to an intermediary you do not even know consists of who. Since we are a community here who understand privacy, I am sure there is nothing to worry about here.