because it wasn't a minority. The Iranian revolution had wide backing, the Shah was an absolute monarch who came to power in a coup. Women and students featured pretty prominently as well. Lots of the tactics today like women opposing the military directly were used back then too.
The revolution had a wide backing, but - importantly! - it was a revolution against the Shah, not in favour of Islamic fundamentalism. The hard-liners were merely the most prepared to step into the power vacuum that followed.
Calling it the "Islamic Revolution", as state-sponsored history books do, is crass revisionism.