Should the US back Israel when it goes after the mullahs nuke factories?

More non-existent factories then. They may as well, it's been a while since the last foreign intervention kicked off, and they were a roaring success.

No. Israel can take care of themselves.

The USA should learn to deal with their internal problems first before even considering to meddle in the rest of the worlds business.
Unfortunately the economy is in too many (ex-)Israelis hands to avoid this to happen. The USA will back Israel in anything when asked, internal structure has been put in place to be certain of that.

On a side note: Israel should not exist in the first place, they lost their land, used a sad puppy story (which is of course not like that) to gain sympathy and thus the USA kicked the Palestines out to make space for the Jews. Kind of unfair. Let's kick the people from the USA out to make space for all those poor people in overcrowded countries... How does that sound? It's the same...

Why shouldn't Iran have the right to use nuclear energy? Because Israel does not want them to? But it is alright for Israel to have hundreds of nuke weaponry. Who f'n died and made Israel police of the world? Israel is a terrorist state, ask a Palestinian or a Lebanese.