The Islamic revolution changed the whole idea of Iran being one of Israel's and America's biggest allies in the middle east to the exact opposite by making the republic an Islamic one, both the laws and the vision of the Iranian government was to be guided from the Islam laws and registration...or so it was meant. Anyway, I don't think there is any country in the world other than Iran that's name contains the word "Islam".
And regarding your question about how did that affect international relations, well lets just say since the revolution Iran lost contact with many countries it had some powerful relations with and made some new ones with some countries that were once considered one of it's enemies.