No one ever said that Christians and Muslims have the same stereotypes. Your strawman is a strawman.
If you ask 10,000 people randomly selected from a Muslim nation if American Christians act privileged, do you think you’ll get affirmative answers? If you ask 10,000 people randomly selected from a Muslim nation if American Christians act violently, do you think you’ll get affirmative answers?
I believe Islamists are portrayed more than fairly by the media. The viewers (including you) must realize however, that although all Islamists are Muslims, not all Muslims are Islamist. In WWII media the Germans and the Japanese were the stereotyped bad guys. In the cold war era the Soviets were the stereotyped bad guys. In post 9/11 media…I’ll let you figure it out. No one is making movies about bad guy Muslims. They are making movies about bad guy Islamists. I have seen moves and media with positive Muslim characters. Unfortunately most Americans don’t like the same movies I do or the movies I like would do better at the box office.