It’s interesting because by all accounts they (Houthis) control most of the population centers of the country despite ostensibly representing the Shia minority that only constitutes ~25% of Yemenis.
Your numbers are wrong. Zaydis (Shia) make up around 50% of those centres. During the rebellion half of the national army fighting the Houthis was Shia (the same sect) as was the former president leading the country at the time.
This isn't a religious war. It's been a lazy media pushing that narrative.
the houthis put iranian military assets too close for comfort for the saudis
Furthermore, the comparison is a bit off because Soviet military build-up on Cuba was merely a response to the actual nukes the US had in Turkey, literally on the Soviet border, but the US lost their shit in a typically hypocritical manner. Iran is purely projecting power wherever it can to combat Saudi and US influence in the region, it isn't a tit for tat response.