No they are not allowed to set the ANY rules and if they do set them they need to be transparent. You will find that discrimination charges can be brought quite frequently where there is suspected discrimination. Try putting no females, no gays, no black people, and see how your rules go.
Well, my issue with setting limits on what someone can/cannot designate on a rule is that you have fuzzy borders.
"No gays" -> Not OK?
"No scammers" -> Not OK?
"No shady individuals" -> Not OK?
"No spammers" -> Not OK?
"No gang members" -> Not OK?
Where do you draw the line? And if it's case-by-case, then does that mean we're just making this up on the fly?