So in the story the ordinary people wanted to get rid of the Shah because the Shad was anti-communist? And I'm assuming all the other characters, like Marji's family, parents, grandparents, etc. held idealistic views of communism?

Marji's parents liked Mohammad Reza Pahlavi who took control of the oil and represented a socialist approach. The US backed Shah took away power from Pahlavi which sparked a revolution. The Shah of Iran was deposed by a strict Islamic republic under Ayatollah Ruhollah Khomeini.