In this same article, Pence said that he would have no problems whatsoever with Syrian refugees being brought to America but only if they were Christians. His issue is apparently NOT with Syrian refugees per se, just that he wants to keep the Muslims out of what he implies is a Christian-only country.
Mike Pence Opposes Word ‘Vice’ On Religious Grounds, Doesn’t Want To Be Called Vice Presidential Candidate
http://www.huffingtonpost.com/christopher-lamb/mike-pence-opposes-word-vice_b_12029434.html

OCU