The “right” and the “right wing” and “conservatives” are the people who wish to maintain the “old regime.” The Old Regime in Iran is the Mullahs and their puppet government. In the US the Old Regime is the Constitution and the Declaration, free markets. etc.
Actually, the "Old Regime in Iran" would be the Shah - the Mullahs are nothing but wet-behind-the-ears, rabble-rousing terrorists. And even a government led by a shah is hardly comparable to "the Old Regime" in these United States, which you suggest "is the Constitution and the Declaration, free markets. etc."