Q: How do I keep shared family members from using my payment methods

You can use "Ask to Buy" to control children's spending.

Request and make purchases with Ask to Buy - Apple Support

If you are referring to the payment of purchases by Family Sharing members, you can only prevent your Credit Card from being used to pay for those purchases by having the members apply a gift card to their Apple/iTunes accounts. If a Family Sharing member has a gift card on their own Apple/iTunes account, it will deduct the purchase from the gift card first. If there are not enough funds on the gift card to cover the item being purchased, or if there is no gift card on the account, the purchase will be deducted from the credit card that the Organizer has on file for their Apple/iTunes account.

Cheers,

GB