Ultimately, acceptance depends on who is processing your payments (e.g. Stripe, Adyen, CyberSource). All Apple/Google Pay do is take advantage of tokenization, which allows buyers to send merchants a token/pointer to an account rather than a real credit card number. Every transaction gets a different card number to minimize risk in the event of a data breach. Additionally, both services make it really easy to checkout by providing a simple method to provide the billing/shipping address in addition to the payment info. No more typing. Just click the appropriate pay button, and confirm payment with your fingerprint/passcode on your phone.
Here is a demo I created for edX: https://www.youtube.com/watch?v=axTCbUjWcbI