There are alternatives, but if your concern is privacy, you won't like them either. Apple. Samsung, Venmo, PayPal, etc. You will have to trust some third party who probably doesn't deserve it.
Crypto was supposed to be the open-source payment method that was totally trustless, but then the tech bros decided they liked Lambos more, and now it is a store of value that people are encouraged to hoard, and not spend. (The worst thing that ever happened to crypto was for the price to go up.)
I think the most private NFC payment method right now is an NFC-enabled physical credit card. It keeps more of your financial life away from the other spies in your pocket. That doesn't keep your credit card provider from selling your info, but they would do that regardless of whether the card is in your phone or not.