It's not about any conflict between USA/UK and the Houthis, it's about protesting at the indiscriminate bombing of civilians in Gaza.
And that protest is aimed at stopping the shipping passing through the Suez, especially any shipping relevant to Israel.
Just the occasional attack is sufficient to re-route the majority of the shipping around the Cape.
Any demonising of Iran for supporting the Houthis, Hamas, Hezbullah, etc, is no different to USA/UK supporting Israel, Saudi Arabia, et al.
It's proganda and as such it's subject to Confirmation Bias.
It's just proxy wars by larger nations. Obviously westerners are subjected to western propaganda, and Iranians, etc subjected to Iranian propaganda.
It's governments, men in grey suits, who never fight, probably very few have ever seen active service, who cause and prolong these conflicts, where the plebeians suffer the casualties.