Comment Also with regards to state schools (Score 3, Informative) 606
Clubs are held to a higher standard. The general student body can get away with a whole lot. You can go and have a racist rant out in public every day and so long as you aren't disruptive, threatening, etc then they can't do anything, they have to let you stay and if a teacher were to retaliate grade wise they could get in trouble. However clubs, like frats, have additional rules imposed on them if they wish to remain school recognized clubs. The school doesn't have to allow them, so they can choose what additional restrictions they face.
Now you are free to have a club not recognized by the campus, but then you won't be able to use campus facilities, participate in official campus events, and so on.