Can you add an adult child with out giving them the ability to use the credit card on file?

Apple is now documenting that a positive Apple account balance (done with iTunes Gift cards) will be charged first, so that is an option.

Where does it actually say that? It would go against one of the primary tenets Family Sharing works the way it does and is reined inside a tight relationship unit by the payment method system. The sections I quote below are specific as to payment methods. As is not unusual in Apple documentation the section you posted is a vague statement by saying "most", unless they are basing this on statistics from their sales department and actually sharing something like that with the public.

How apps, content, and subscriptions from Apple are billed - Apple Support

"Some purchases aren’t charged to your Apple ID balance

• If you're in a Family Sharing group, purchases are charged to your personal Apple ID balance. If you don't have enough Apple ID balance to pay for the purchase, the remainder is charged to the family organizer's primary payment method."

and:

"The primary payment method is at the top of the list in Settings on your iPhone," with a link to:

Change, add, or remove Apple ID payment methods - Apple Support which shows examples in the first image. The top part shows the person's Apple ID balance, below that they are all cards of some sort. At this point Apple's sometimes poorly worded and badly cross-referenced documents add confusion to interpretation since the top of the "list in Settings" is the Apple ID balance. However, the image also includes text, "The payment method below your Apple ID balance is used for purchases made by family members." I think "the list" really means "the list below your Apple ID balance".

I don't see where there is any mention of purchase sharing being linked to payment method used. Purchase sharing simply presents the option to let others share what you have bought, or not. "When you turn on purchase sharing, everyone in your family gets access to the apps, music, movies, TV shows, and books that family members buy from Apple."

Big Al the Eagle wrote:

Family sharing with adult kids and not using the credit card on file. It makes since to do the family plan of “Apple One” but they have there own payment methods to pay. I don’t want them using my card for there purchases. Thoughts?

don't enable purchase sharing.

My thought is you can't do it how you wish. You can't place an "Ask To Buy" on an adult account. Anything they buy that goes over any available balance in their account will be charged to your card. That's how Family Sharing works. Get them to make sure they always have sufficient balance by adding value to their accounts so your card is never charged.

Add money to your Apple ID balance - Apple Support

Create and add money to an iTunes Pass - "At Apple Stores and select retailers, you can add store credit directly to the Apple ID that you use for App Store, iTunes Store, and iBooks Store purchases." - https://support.apple.com/HT203021

Limnos wrote:

"I don’t want them using my card for there [sic] purchases. "

Purchase sharing just handles if something will be shared or not, not how it was paid for originally.

Purchase sharing is tied to the organizer's payment method. If disabled the organizer's payment method is not used.

Apple is now documenting that a positive Apple account balance (done with iTunes Gift cards) will be charged first, so that is an option.

"I don’t want them using my card for there [sic] purchases. "

Purchase sharing just handles if something will be shared or not, not how it was paid for originally.