Question

Why did the United States support Mohammad Reza Pahlavi, the Shah of Iran, despite his extreme unpopularity in his own country?​

Answer 1

The United States did not support Shah Reza Pahlavi nor did they oppose him. The United States foreign policy prior to World War II (when Reza Pahlavi ruled) was minimal and therefore most American administrations did not have an issue or position with his leadership.

The United States would come to support his son and successor Mohammed Reza Pahlavi as the Shah of Iran. Hope this helps :)