This is a bizarre argument. Secularism and westernization in Iran during the 20th century were almost entirely a result of Reza Shah's reforms, as well as his closeness with the British monarchy -- itself a parliamentary system.
> Iran had a large communist movement
By the time of the revolution the Tudeh party and other communist groups were quite weak. They contributed to the upheaval without having any credible chance of installing their own leadership in the country.
> Initially the Shah supported the ayatollahs
This is a rosy but false claim. Khomeini and Khamenei spent a collective 18 years in exile under the Shah, and faced house arrest while in the country. The Shah arguably gave ground away from his own power base (aristocrats) during the White Revolution, but arguably this was intended to subdue anti-monarchical sentiment and solidify his power. That doesn't mean he "supported the ayatollahs."
The US (and UK) replaced Mosaddegh with the Shah. Then the Shah and SAVAK (with CIA help) launched a decades long attack on the secular, parliamentary oriented forces in the country. Initially the Shah supported the ayatollahs, and in turn was himself tacitly (sometimes openly) supported by them. Eventually they turned against the dictator under the spell of a foreign power.
Also, Iran had a large communist movement, and it is obvious in 1978 and early 1979 that the US, UK and France saw the communists as the enemy, Khomeini as someone to disempower but not destroy, and the Shah as who to support as long as they could. So that stance helped Khomeini on some level. France would not have allowed communists to sit in France and work successfully to undermine a friendly power (even Indochina, although that stance loosened in the 1950s).