The Iranian Revolution was not about the veil.
It was not about Iran being pushed towards 'freedom' too fast by the American 'friends' of the Shah either.
The Shah's regime was one where personal control rested essentially with the Shah. He played groups within the power elite against each other to prevent any threat to himself from developing within that group (army officers, etc.)
His regime was set in place by the CIA, bolstered and advised by the CIA, and was used by the US to fight the Cold War and keep oil flowing to the west. The oppression of the secret police therefore was focused on the leftist opposition to the Shah, the Iranian Communist party and others, while the religious opposition, which the US did not see as a threat, or understand, remained comparably free to operate under the radar. There was a disregard fro Islamic tradition, notably in the introduction of a new calendar whose starting point was the birth of Cyrus, as opposed to the former Mohammed-centered calendar.
Under the guidance of the CIA the regime was corrupt, brutal, and oppressive, and one of the tipping points was the introduction of diplomatic immunity from prosecution for those CIA operatives who were responsible for the brutality.
Additionally, the regime's extravagance was in sharp contrast with the lives of most Iranians, especially in 1977-78, when inflation hit hard and austerity measures were introduced despite the fact that Iran had reaped a huge windfall from oil revenues in the early 70s.
The regime was not heading in the direction of more freedom for anyone except US business and political interests. It was opposed by many and varied factions throughout its history.
Iran has had a long relationship with the veil and the symbolic use of the veil for political purposes. It was first banned in Iran in 1937, resulting in much uproar, and then restored in 1941. From then on, the veil was manipulated by political groups (it was never the central focus of any group or a major issue in and of itself) When the Revolution began to gather momentum in 1978-79, women took to the streets in huge numbers, using the veil as a symbol of their opposition to the regime -- the regime collapsed and within a month of his return from exile in Paris, Khomeini issued a decree requiring women to veil in public (March 1979).
The next day, which was International Women's Day, enraged women took to the streets and continued to protest against the repressive policy of the new regime for quite a while afterwards, to absolutely no avail. The protests were massive and spontaneous -- and received no support from the political groups Iranian women had strengthened in the leadup to the revolution. Veil-wearing was strictly enforced by enthusiastic misogynist zealots.