In this interview with Sheikh Omar Bakri Muhammad, we see one picture of what a Muslim-ruled America would look like.
What would be the rights of Christians in a restored Caliphate?
As citizens, in terms of welfare and security, education, etc., they will be equal. They will be exempt from national service, although they can volunteer. They will pay the Jizya poll-tax for security and signifying that they submit to Islamic law, except if they join the army. This need not be levied with humiliation. Nor is it levied on women, children, clergy, elderly, etc., only on mature, working males.
No private schools will be allowed, and there will be an Islamically influenced national curriculum. No new churches will be permitted, but existing ones will be allowed. Private consumption of alcohol will be permitted, but not its public sale. All state officials must be Muslims, save for the Caliph’s assistants to advise him about relations with non-Muslim citizens. Muslims could not convert to Christianity on pain of execution. Evangelistic campaigns would be forbidden, but people would be free to present Christianity on TV, in debates, etc.
Sound like the situation for Christians in Egypt.