You need to think beyond first order effects.
Saudis want to get rid of Iran, for Shia-Sunni reasons.
Israel wants to get rid of Iran because of the 3 Hs.
Enemy of my enemy is my friend and all that; that's why KSA and Israel mended fences (for now).
Now Saudis cannot take on Iran at all; heck, they can't even take on the Houthis. So ... they found the 800lb gorilla (USA) and convinced it that those mean Iranians had made stupid faces at him.
Iran, meanwhile, showed colossal stupidity and arrogance by supporting these 3 Hs. Houthis, I can understand; they are going after Saudis mainly. But Iran had no dog in the Israel-Palestine fight!
