The Houthis began their rebellion in response to Salafis (who are Sunni) encroaching in their region, interfering with their way of life, building Madrasas and pushing their brand of Suna - just like said Taliban does. But since then it's been about territory, resources and political control.

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.