So is there anything like a decentralized exchange for Bitcoin where you can get current market price and exchange stablecoins with Bitcoin with other people? Or any other good buying option that preserves privacy?
Have you tried bisq or hodlhodl?
You can do your research on what stable coins are transacted on either platform, and the fee is a certain percentage of the total transaction, about 1% (+/-)
Your privacy is somewhat preserved as it's a peer to peer platform.
You'll however still have to take necessary precautions, like using a coinmixer if you don't want the source of the bitcoins to be traced and practicing safe browsing.