Are there examples of iOS apps that use native subscriptions to pay for memberships? I have a client that has a membership card that gives discounts in restaurants, and wants to take payment through the phone. However apples ToS seem to explicitly forbid gym memberships, so I'm curious if that means all memberships are disallowed or if there are cases where this is done. 

Otherwise we'll probably use PayPal.

In app purchase guidelines: https://developer.apple.com/in-app-purchase/In-App-Purchase-Guidelines.pdf page 7 explicitly disallow gym memberships.
You can't use In-App Purchases for that. From earlier in the In-App Purchase Guidelines:


  You must deliver your digital good or service within your app. Do not use In-App Purchase to sell real-world goods and services.