From what I have read/heard, this can be tended to by not regarding as a first amendment speech issue, instead taking it to a level of discrimination which is something which would hold water. The persons on the video said they'd never allow certain persons in. If they had kept quiet, people could have held a presumption that they were discriminating, but would have had to work at finding solid proof.
Good to see them booted out of the frat and the quarters they were staying in. As to the continuance or lack thereof, in their educationing at OU, that's a matter which clearly they have to address. Not sure what their policies are, there may be something written which all students are to abide by, which prohibits any form of discrimination.