Not really. Most Americans know little or nothing about Orthodox Christians, much less harbor fear and hatred for them.
Knowing little or nothing about often goes with prejudice and hatred of, though it was not “most Americans” I was referring to, but the secularist “elites”, particularly in foreign policy: every conflict between Orthodox Christians and Muslims has the U.S. siding with the Muslims, or at least winking at their aggression (e.g. Cyprus). If broadened to Eastern Christians v. Muslims, the sole exception was Nagoro-Karabak, where the U.S. backed the Armenians against the Muslim Azeris.