The Saudi government’s decision this past week to lift its 35-year ban on movie theaters delighted entertainment lovers across the kingdom. But for a small band of Saudi liberals, who look to cinema and other media as means to effect social change, it was a particularly sweet moment.

For decades, liberals in Saudi Arabia and other Arab countries have championed religious and ethnic pluralism, women’s rights and the rule of law as building blocks of security and prosperity in their societies. Outsiders often discounted them,…