Can my family use Pro with Family Sharing?

The Pro screen says: One payment, yours for good, no subscription. Family Sharing included. Family Sharing is included for Pro.

SkipTube itself does not treat a family member in any special way. Pro is checked for each SkipTube account, in the store.

If someone in your family bought Pro, sign in to your own SkipTube account. Open the Pro screen and tap Restore purchase. If SkipTube finds a purchase, Pro turns on. If it says Nothing to restore, it found none for that account.

Pro is one purchase, so a restore moves it to the account you are signed in to. See Restore your purchase.