Shared subscriptions are handled separately from shared purchases. See Turn off purchase sharing and stop sharing a payment method. As a not the organizer you can opt not to share your purchases, however the organizers payment method may still be charged for any purchases that cannot otherwise be taken from store credit attached to your account. If you want to be able to use your own payment method for a specific purchase then you need to ask the organizer to turn off purchase sharing from their account, at least temporarily. I do this sometimes with my now adult children, but I'm generally happy for them to buy stuff on my account.
It doesn't appear to be made clear anywhere, but you can only leave and join a family once per year. Leaving the family in order to workaround a payment issue might not be the best approach, should you be thinking of it.
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