Is your purpose in drawing this distinction to claim that the secular tendencies of the population of Iran is an effective counterweight to the ambitions of its theocracy?
US ambitions keep the theocracy powerful. Since they overthrew the US backed dictator which had overthrown the secular, progressive democratically elected government of Mossadegh.
Every time the US threatens Iran or imposes sanctions, or funds and arms a terrible dictator in Iraq so he can bomb Iranian cities and drop poison gas on them killing hundreds of thousands of people. The theocracy steps up to the plate the only force powerful enough to stand up to the US.
Any more liberal voices get drowned out by the need for security from the US and its interests.
Islamic Republic of Iran is a theocracy.