They are not that innocent either.
Its power games and geo-politics. 65% of Yemen is Sunni. Saudis supports a group that's ideological aligned to them and are majority in the country. Iran supports their favored group which is ideologically aligned to them. All those weapons that Houthis have are provided by Iran.
Now, its a national security matter for Saudis as its their backyard and their one of most important economic artery (bab al mandal strait).
If I'd be Saudi, I'd have genuine national security concerns on Iran supporting an armed militia in my backyard.
But anyways, I have always maintained that this conflict needs to be settled with talks.