I never gave it much thought. I mean, my fraternity is coed, and when it was founded it was a women's fraternity (and that was the term used,
not sorority), and people who don't know about it (other than that I am part of it) always refer to it as a sorority. Which I don't like because it is misleading and leaves out a lot of very important people, but I don't take it personally. Usually I just inform them.
As far as frat vs. fraternity, I
think that typically in my spoken communication I use the term "fraternity", but I know that I usually shorten it to "frat" when typing/writing/etc. That's just laziness though

. I can see where the shortened term may conjur up some negative stereotypes, but I also think that most of the time if it
does do that, then it is because that person already has those stereotypes in mind. They would probably get the same idea either way.
Regardless, it's great that you have pride in your GLO (<---see! more laziness

) and
not because it's a party house.