Freedom of religion does not apply to immigrants only citizens of America, and technically they can be turned away for any reason whatsoever or no reason at all.
I think this refugee debate has gone off the rails and peoples mere concern for who these folks could include has sounded alarms of bigotry. But still think about it, the Muslims that are coming from this location are leaving the incubator of extremism, I don't think its unheard of to slow the influx and seriously take a look at them.
Is there a difference between a christian Syrian refugee and a Muslim?
Fundamentally speaking based on their ideology no.
One's groups beliefs actively promote things contrary to the constitution, in other words they don't agree with america. Tough situation. I already lived in a neighborhood that was probably about 75% Muslims from Egypt. Palestine, Syria and Lebanon, and 25% Christians from the same area. Based on my many years there and what I saw, if I had my choice of neighbor it wold only be one of that group.