When you sign in to tv.apple.com for the first time, you may be asked to add or verify a credit card to ensure the account holder has authorized viewing on the web.
Parental controls for Apple TV+ on the web - Apple Support
This verification will try to match the card on file as payment method, and according to user reports, it will accept debit cards for that, if they match.
When you log in to tv.apple.com on the web next, Apple TV+ remembers your parental control preferences across all web browsers. Content restrictions set through parental controls on tv.apple.com do not apply to Apple TV+ in the Apple TV app on iPhone, iPad, iPod touch, Apple TV, Mac (Catalina), smart TVs, or other streaming devices.