I don’t see anything discriminatory about an Ashkenaz school not taking Sephardic kids. A religious school is intended for those who follow the same religious practices. Sephardim have their own halachos, their own poskim, and even their own derech halimud.
As far as Chabad, that’s a very involved discussion. The reality is that many Litvish gedolim have a very big problem with them.