"Do you think a politicians personal beliefs are anyone's business?"
Without a doubt.
"Shouldn't their political ideas be all that matters?"
No. Let me ask you something, if a candidate was a member of the KKK or a racist skinhead movement, do you think that should be your business as a voter? You think that might have some influence on the politicians political views or do you think that should have no bearing on anything? A candidates personal views are a clue as to what type of person that politician is.