That a political figure may use religion does not negate religion as a basis of conflict between peoples and parties. Often all that such politician is doing is following what the religious push under them is seeking among the people. Often such a politician is FOLLOWING the religious basis of the conflict. That does not make the basis of the conflict “political”.
As for the Mullahs of Tehran they are all about their religious beliefs, and because of those beliefs they don’t care about the politics of whomever they work with, for the Mullahs own religious ends. For them their religious beliefs are their power, the basis of their power, and the power they seek to build in the rejoin. You can see politics all you want, they see religion.
Religion is sometimes just the clothes they put on -- exactly the point I've been making. The overthrow of the Shah was only possible through violence, using (not by coincidence) the same violent methods used by every despotism that rises to power.