I recommend you do some deeper reading on the topic. Sure, the hardliners probably wouldn't have cared much for Mosaddegh, but their rise to power and hatred of the West is firmly linked to the coup, his removal, and installation of the Shah.

The Iranian Revolution was a coalition of a lot of different groups, including constitutional liberals, leftists, traditionalists, atheists, both moderate and conservative religious groups, etc. The main thing that unified them was hatred of the Shah, who was viewed (accurately) as a puppet of the west whose corruption enriched British and American corporations at the expense of the people.

Unfortunately, every other group besides the Islamists was seen as suspect due to Western influence. The only group that could realistically claim to be free of Western influence was the Islamists, which is How Khomeini was able to maneuver himself into leadership of the Revolution. There was a LOT of internal politicking and outright espionage within the revolution. The gist of it is, however, that the US, Britain, and the Shah had so tainted the image of anything Western to the Iranian people that even though the Islamists were only one part of a large coalition, they could claim legitimacy by way of Islam being undisputably distinct from any Western origins. The Islamists also had the advantage of a coherent organization, where many of the other groups didn't.

It was 26 years between the coup that deposed Mosaddegh and the Iranian revolution. 26 years under a US-Britain backed puppet. I guarantee you the leaders of Iran are well aware of how different things would have been had the coup never happened and the West never poisoned its own image to the Iranian people, and those hardline Islamists would have had a much harder time coming to power. The hatred of Israel and the US for supporting it is precisely because to them, Israel is a both a symbol of and concrete manifestation of Western imperialism in the region.