Can you put a keep private option to displaying your fantasy teams in your profile settings? I think users should get to decide on what profile information should be displayed.
That is a bad idea. As a Commissioner, I try to view an owner's leagues before allowing them to join one of my leagues. Eliminating this ability will lead to problems in many leagues trying to fill vacancies with good owners.
Then have the owner set their history to public. What's wrong with having an option?
I would be leery of an owner with a private setting. If they wanted in one of my leagues, they would more than likely be denied. What would that owner be hiding?
Call me crazy for advocating an option for privacy. In your case just make it clear that a profile must be public to be considered join your league.
Assuming you have a facebook, do you have all pictures, history, address, phone, gps, etc set to public where anyone in the world can view it? If not, what are you hiding?