I know we differ significant when it comes to using centrazlied/decentralized exchanges and our approach to KYC, but even when only discussing centralized exchanges I completely disagree with this statement. Coinbase admitted they were selling customer data to third parties. Coinbase bought out Hacking Team, which manufactured and sold surveillance software to human rights abusers. Coinbase have partnered up with the IRS, the DEA, and the Secret Service. There isn't an entity in cryptocurrency I would trust less than Coinbase with my data.

For OP, as others have said, your issue here is that the fiat side of your transaction is forcing you to complete KYC. It is entirely possible to buy and sell bitcoin without completing KYC, but it does take more effort and work to do than simply opening an account, uploading your passport, and making a trade. Essentially, you need to trade peer-to-peer with other individuals rather than going through a central service like Coinbase or Binance. There are several ways to achieve this. The ones I use predominantly are BISQ, LocalCryptos, or the currency exchange board on this forum. You will need to be able to pay in other forms of fiat to another person, be that cash in person, money order, bank transfer, PayPal, or something similar. You will also need to spend some time reading about the security and escrow measures for the first two, or finding a reputable trader or reputable escrow if you are trading with someone on the forum.

As I said, it takes more time and effort, but I absolutely feel it is worth it to avoid compromising your privacy.