Actually really the only thing that really precipitated the hostage crisis and enmity with the US during the Islamic Revolution in Iran was the following:
"On October 22, 1979, at the request of David Rockefeller, President Jimmy Carter reluctantly allowed the Shah into the United States to undergo surgical treatment at the New York Hospital It was anticipated that his stay in the U.S. would be short; however, surgical complications ensued which required six weeks of confinement in the hospital before he recovered. His prolonged stay in the U.S. was extremely unpopular with the revolutionary movement in Iran, which still resented the United States' overthrow of Prime Minister Mosaddeq and the years of support for the Shah's rule. The Iranian government demanded his return to Iran to stand trial but the U.S. government refused to turn him over" -- from a wikipedia article on the Shah.
If we'd have pretty much thrown the Shah under the bus, things might have gone very different. Basically Carter not sitting on his hands waiting and basically telling Brezinski to go fuck himself since Brezinski was pretty much wanting to go on a full scale invasion of Iran to re-install the Shah.We probably would have had a continuing relationship with Iran much like we do with the Saudis.
IIRC as a side note, once things got really torqued up there was some wavering on which embassy to take; Believe it or not, Ahmadenijad (who was one of the hostage takers at the time) was more for going after the USSR embassy than the US embassy. Interesting POD if they decided to take the USSR embassy instead of the US.