Family Sharing without Credit Card

According to the "Start a family group" section in:

Set up Family Sharing - Apple Support

"One adult in the family—the family organizer—can set up Family Sharing for the group from their iPhone, iPad, iPod touch, or Mac. If you turn on purchase sharing, you'll be asked to ..."

So, it seems to me if you don't turn on purchase sharing then you should not need a credit card. But I may be wrong.

You are welcome. Note that the link talks about methods you can you use with your Apple ID. The organizer of a family group must provide a payment means that can be used with the organizer's Apple ID for paying for things purchased for the group.

See Payment methods that you can use with your Apple ID https://support.apple.com/en-us/HT202631#uscanada And, see the general link posted above. Set up Family Sharing