Watch out- personal opinion coming.
I honestly don't care what other people do with their own letters. I might have a problem if someone was wearing MY letters and out acting the slut or something, but there's really not a whole lot I can do about it.
I would probably not let another girl wear a shirt with my letters on it (especially when I have so many without letters). But, I would also not let someone be cold rather than wear them when there is no other option. That is just human decency. Anyone who puts their letters above a friend has bigger problems to deal with.
I have no problem whatsoever in seeing a man wear my letters, or letting a man wear my letter shirts. Keep in mind that I am talking about casual letters- no man (and definately no woman who is not a sister) will be wearing my badge or my crest. There is just no reason for that as far as I am concerned.
I would also never wear another sorority's letters if I don't have to. I had an ex one time who's apartment was ALWAYS freezing and the most compfortable sweatshirt he had was an old Tri-Delt date party sweatshirt- so I wore it inside out (but never in public).
I never have and never will see any reason for me not to wear fraternity letters (shirts and such), but I also don't think I would wear my boyfriend's badge. I also see no reason for that, just as I see no reason to wear another sorority's badge.
For people who maybe wear their husband's badge- I thought lots of orgs make "sweetheart" and "wife" pins. Maybe I'm wrong.
I just remember my ex saying that they consider their greek letters very special and there are only a select few places that THEY can even have the greek letters. He specifically told me that the only women who get to wear their greek letters are (i think) wives and mothers. And I believe they had a special pin for those. Again, I COULD BE WRONG.
Ok, end of personal opinion.