The Yemenis are being punished for being primitive, xenophobic, and under control of the crazy Ayatollahs.
The Yemenis are being bombed and starved for being
primitive = poor and not having extractable oil
xenophobic = resisting domination by Saudi Arabia and their Wahhabi fundamentalism
under control of Iran = Iran has provided some weapons and aid to both assist fellow Shiites and be a thorn in Saudi Arabia's side. But the Shiite religion in Yemen is distinctive and different than the 12er beliefs of Iran, and the idea that Iran is calling the shots is just US/Saudi propaganda, partly designed to promote the war against Yemen and partly to justify harsher actions towards Iran.
Yemeni religion and politics is all its own thing, despite foreign interference. I haven't seen a credible source that believes Iran is pulling the strings in Yemen or has much influence over the Houthis.
Of course, the Yemen War is part of the Saudis attempt to expand their regional power, which reportedly America First Trump has encouraged. They kidnapped the Prime Minister of Lebanon. The ex-head of Yemen resides in Saudi Arabia claiming to be the lawful ruler, and can be expected to do Saudi bidding if they ever reinstall him.
Choosing between Saudi Arabia and Iran, at least one of them has active democratic elections, though we only care about such things when it suits our purposes.