I don’t want a payment method
I don’t think my payment method is any of Apple‘s business. They do not need it.
Apple Wallet is totally voluntary as is the use of Apple Pay. Just don’t add any cards to Apple Wallet app. If you’re referring to Apple requiring a payment method be added to your Apple Account, that is an Apple requirement to download most apps, even free apps and to use many of the services such as iTunes, Apple News etc.