Is the enemy of my enemy, etc. etc... ? Apparently not.
We have heard Yemen described as a proxy war between Saudi Arabia and Iran, and I suppose that's accurate enough a description. We've also heard it described as an outgrowth of the classic Middle Eastern conflict between Sunni and Shi'a Islam. That, I'm pretty sure, it is not.
The Houthi are adherents of the Zaydi sect, which is an offshoot of Shi'a Islam, but not nearly orthodox enough to satisfy the clerics who hold power in Iran. Iranian Muslims supporting the Houthi because they're, sort of, Shiite, would be kind of like the Roman Catholic Church supporting Seventh Day Adventists because they're sort of... well, you get it.
Move over to Iraq, and you find Sunni clients of the USofA fighting the Sunni zealots of Daesh, aka all those other names and acronyms tirelessly repeated in the American press. Why are Sunni fighting Sunni? Not because IS (aka etc. etc.) is especially naughty what with the beheadings and whatnot. No, it's all about the usual, just as it was from the time of the Cheney invasions or even the CIA's 1953 overthrow of the democratically elected Mosaddegh government in Iran and installation of the Shah.
It's about the oil.
That's why Saleh could be fighting the Houthi one minute and supporting them the next. That's why the Egyptian military, an equal opportunity oppressor of Islamists no matter what branch of Islam they spring from, is out there trying to restore Hadi to power. That's why Americans, even some in government, are having such a hard time figuring out how and why anybody is putatively allied with anybody out there around the Persian Gulf.
Don't be confused. Just follow the money. Follow the oil.