I'm sorry, I figured taking a train load of people hostage or repeated bombings of public transport would be equivalent enough.

The Houthi, and other Zayidi Shia groups, have been discriminated against legally and culturally since the at least the 80s. (At least in part a response to Zaydi rule during the Ottoman Period).
I can't find straight ethnic group numbers, but most sources state them to be a minority, so I'd assume that that's the largest single smaller than 50% group. And given the diversity of peoples in Yemen, makes the religious aspect more important.

Not all good though, the Houthi movement could (should) be doing better on treatment of Bahaï and Jewish people, and the treatment of women could be better, but the Houthi forces are also engaged in combat with Al Qaeda, who would be much worse.