NIC membership does say something about the organization in that it has met certain requirements, is organizationally pretty stable, etc. Not that Kappa Sigma or Lambda Chi Alpha have any problems because of their lack of affiliation.
There is a little context, which I think, if true, could mitigate some of the concerns a little bit. The students claim that the video of the gentlemen saying the racist things was part of a skit roasting a brother who was a conservative Republican--a student, they claim, who doesn't hold those views despite his political affiliation. If that's true, there perhaps wasn't a racist intent or any attempt to marginalize anyone other than, ironically, conservative Republicans. It does remind me of a Dave Chappelle sketch in which a blind black man, who apparently doesn't realize he's black, is the head of his local KKK chapter, While I'm not by any means comparing the talent or the level of irony achieved in the various sketches, if the students' explanation stands, is this something they should be expelled from school over?
https://www.cnn.com/2018/04/23/us/ne...rat/index.html
The second video, I expect will have a similar explanation.
Syracuse is a private school though, so they can give any person or organization the boot. They're currently reviewing all of Greek Life.