We’re not supporting the anti-houtsis in Yemen either.
The anti-Houthis in Yemen are, a lot of them, Al Quaeda, the guys we have been bombing.
That is another Sunni-Shiite war a la Iraq, with some very similar players, or rather a three sided war (at least).
Lucky for the Saudis is that the Houthis have the north of Yemen and the Sunnis the south, so the AQ types have to get through the Shiites to make trouble in Saudi. Its sort of a religious geographic sandwich.
Its an unholy mess anyway.