Well, to be fair, Iran has legitimate grievances against the West even aside from the Palestinian cause. The whole Mossadeq episode, followed by the brutal Shah regime and Savak, had nothing to do with Israel and that alone is reason enough for the Iranians to hate the US and UK.
The Israel issue is something that Iran championed because of a vacuum: where the Arabs and Turks couldn't even whimper in protest. Iran saw an opportunity to position itself as a champion of the Muslim world. Whether the support is cynical or in earnest is a matter of opinion.
What is ironic is that Iranians are at least respected in the US, maybe because of a large influential diaspora of Iranian Jews and Armenians, but the Arabs, Turks and Pakistanis elicit only derision in popular American culture.