Unless you are the Organizer your payment method cannot be used. Only one person, the Organizer, can (and must) have a card, but the Organizer can avoid having this charged by others by asking them to make sure they have adequate personal balance (e.g., from gift cards) to cover their purchases. Other family members can only pay for things by using their personal balance or by letting the remainder automatically roll over to the Organizer's payment method (such as a credit card but not the Organizer's personal account balance).
The alternative is described in this document: Add a family member to your shared subscriptions - Apple Support
"If you're the family organizer and you don't want to pay for family members' purchases and subscriptions, you can turn off Purchase Sharing [ How to share apps and purchases with Family Sharing - Apple Support ]. When Purchase Sharing is turned off, everyone must use their own payment method. When Purchase Sharing is turned off, family members can share subscriptions, but they can't share individual purchases like apps or books."
Ref:
- Family purchases and payments - How to share apps and purchases with Family Sharing - Apple Support
- How apps, content, and subscriptions from Apple are billed - How apps, content, and subscriptions from Apple are billed - Apple Support
- Add a payment method to your Apple ID - Add a payment method to your Apple Account - Apple Support
Adding funds to your Apple ID balance:
- How to redeem your Apple Gift Card, App Store Card, or App Store & iTunes Gift Card - Apple Support
- Add money to your Apple Account balance - Apple Support
If you are the Organizer and an app or feature on your device is not working, not appearing, or is restricted (grayed out), it may have been disabled using Screen Time, or by an IT administrator if you are using a device owned by an employer or educational institution.
- Read this support article If your Apple ID or other options are greyed out in Settings —> If your Apple Account is grayed out in Settings, or you can't sign out - Apple Support