I am fairly certain that my abortion position hurt me, because in a Democratic primary, where turnout is relatively low, liberal voters turn out in disproportionately large numbers and thus exercise a disproportionate influence on the outcome.
If a candidate for president said he believed that space aliens dwell among us, would that affect your willingness to vote for him? Personally, I might not disqualify him out of hand; one out of three Americans believe we have had Visitors and, hey, who knows? But I would certainly want to ask a few