My wife and I have separate Apple IDs. To simplify (!) things a while ago we both started using a third ID.
Now with Family Sharing we can each access the other's purchases.
So I set myself up as the family organizer, invited Laura, and invited the 3rd account.
Well to accept the invitation for the third account, I would have to sign out of iCloud, loosing a bunch of data, or possibly having merge problems later.
The invitation has to be opened in Mail. I try not to use Mail. I certainly didn't want to not only sign out of iCloud, but also configure yet another account on Mail. (The third Apple ID forwards to both of us.)
What to do?