Yes, of course the Constitution is compatible with Christianity and most other faiths, for that matter.
Muslims who allow or promote violence against, imprisonment or execution of those who preach Christianity or any faith but Islam would not find our Constitution compatible, however.
Isn't it interesting that Christianity thrives when Christianity ISN"T declared the religion of the state.
Faith cannot be "established" or decreed..much less enforced. Professing a belief means little when a State declares only one belief can be accepted.
Interesting, but not surprising. It's like that with the economy too. The best way to have flourishing institutions is to keep them free from government regulation, supervision, or subsidies.