Should Personal Beliefs matter in Politics?

We like to believe that a person's personal beliefs shouldn't be a bar to their participation in politics. Yet we fairly widely believe we wouldn't elect a white supremacist to office these days. I would add these days that people who are openly dreationists or global warming deniers should no more be considered for office in this country than a Holocaust denier, particularly for the office of President. The President has a major role in setting science policy for the country, and someone who has that poor a grasp of science should not be in that role. I say this because of just having seen in an article that Bobby Jindal is a creationist, and we know from the last election that other Republican candidates are as well.