Question

What was one objection of the ayatollahs to the rule of the shah of iran?

Answer 1

Reduced influence of religion on the government  was one objection of the ayatollahs to the rule of the shah of Iran.

Ayatollah Khomeini served as the supreme religious leader of the Islamic Republic of Iran in 1979, after several years of resistance to Shah Pahlavi. After his appointment as Ayatollah, Khomeini strived to remove the Shah from power for his associations with the West. Upon the success of the revolution Ayatollah Khomeini was appointed religious and political leader of Iran for life.

Answer 2

Reduced influence of religion on the government. The ayatollahs are radical Shia Muslims. They were/are desperate to inflict Shia Islam at every level on their civilians. 

Hope I helped :)