The United States routinely excluded refugees who happened to have been Nazis. In fact, every so often someone is still getting deported because they were a Nazi. Again exceptions were made for Nazis who were willing to serve American interests (the CIA and NASA are infamous for recruiting such persons).
Most Syrian Muslims are very bigoted against both Jews and Christians. The main reason the liberals “love” them is explained by the “enemy of my enemy is my friend”. The US should welcome religious minorities fleeing Islam, and Islamic defectors rejecting the normative (what we call “radical” to be polite) and dominant version of Islam. But the typical Muslim refugees who has not rejected Islam should be given humanitarian assistance, and sent home when the war ends (or when an Islamic country accepts them).