Hello Charlie_Bednar,
Thanks for asking the Apple Support Communities about removing your payment method. I will be happy to help out.
Yes, with an active subscription, your account has to have the payment method. If you can't remove your last payment method or use no payment method with your Apple ID - Apple Support
"If you have any active subscriptions, you must have at least one payment method on file other than Apple ID credit."
If you are no longer using Apple Music, you can ask AppleCare to see if there is an option to help you remove your payment method without having to wait for the subscription time to expire.
"If you tried these steps and you still can’t remove your last payment method, or if you’re unable to remove a payment method, contact Apple Support."
Thanks and have a wonderful day.