They don't want to do anything that would tend to prop up an Arab state right next door to them. Iranians are Persian; ethnicity counts for a LOT.
Blood is thicker than religion in this instance; plenty of Iraqi Shias fought hard (including Shia generals) against the Iranians in the Iran-Iraq War.
Arabs and Persians really, really, really, really, really, really, really, really dislike each other, which is amusing because Americans often confuse Iranians with Arabs. And to an Arab or Persian, you can tell one from the other simply by appearance easily, even though we can't.
But, I thought we were the evil racists?