I can understand there being some amount of value in gender specific communities, but I don't see why including nonbinary people really has to be in contradiction with that. It seems like, by and large, the members of the sorority actively wanted the person involved to be a member. Having a higher authority come in and tell them that they can't do that seems pretty dumb.

If the members themselves decided they wanted to keep the organization exclusively female, I wouldn't really fault them for that; not every space is for every person, and that's okay. I wouldn't want to intrude on a Black social group, nor would I exactly want women to be in a space explicitly designated as being for gay men, for instance. But since the members do want the nonbinary person be in their group, I don't see any real justification for it other than bigotry from the governing body.