The Houthis are very misunderstood. They’re not really “Shia” or “Iranians” or any of that crap. They’re not even really Shia. Ansar Allah, the army of the Houthis, is simply the former Yemeni Army. Probably 80% of them went over to the Houthis and they took most of their weapons stocks with them. The Yemeni Army was mostly Sunni.
There’s barely any difference between Shia and Sunni in Yemen anyway. The Yemeni Shia practice an odd form of Shiism that is very close to Sunnism. Yemeni Shiism only differs from Yemeni Sunnism in only one or two issues of doctrine.
The Houthis themselves are not even necessarily Shia. Most Houthis say they are Shia, but some say they are Sunnis, and a few say they are both Shia and Sunni.
A Yemeni friend of mine told me that before 2014, there was no such thing as Sunni and Shia in Yemen. They were all just Muslims. But Saudi Arabia, the UAE, Jordan, Egypt, and Sudan all went to war against the Houthis, who overthrew the government in a very popular revolution. They also imported Al Qaeda and especially ISIS and for the first time in forever, the Sunni/Shia distinction became highlighted because these genocidal religious bigots decided to make a big deal of it. But it goes against Yemeni history.
In case you are interested, the ousted president was a Houthi, too. As was the previous President who was also ousted. But he was a pro-Saudi Houthi, and that makes all the difference. Ansar Allah are anti-Saudi Houthis. The Houthis ran Yemen for hundreds of years with no problems at all. For most of the last millennium, the Houthis ran Yemen. They’re the ones who know how to run the country. It’s not so much that your average Yemeni Sunni cares anything about the Houthi and the Shia of Yemen. On the other hand, they do have the usual Sunni Arab paranoia of Iran.
The war against the Houthis was really just another Saudi-UAE “Kill the Shia” war driven by Sunni Arabs’ utterly insane hatred and paranoia of Iran.