How do I delete payment methods from my Apple ID on my iPhone?

I have a credit card and PayPal on my Apple ID in Payment & Shipping on my iPhone. I want to delete them both but can't delete either one. Neither the "Delete" button when swiping works, nor does the "Remove Payment Method" link when I go into each individual payment method. It's like they're dead links. I have one active subscription, but I've cancelled it so it'll expire in a few months.

How can I get these accounts off my Apple ID?