The problem is that the politician who honestly holds a popular irrational belief (assuming said belief isn't directly related to the mechanisms of election campaigns) is better able to signal it and thus more likely to get elected than the politician who merely false claims to hold it.
I'd expect politicians to be much better at occlumency than the general population, though.
Suppose I told you that I knew for a fact that the following statements were true:
You’d think I was crazy, right?
Now suppose it were the year 1901, and you had to choose between believing those statements I have just offered, and believing statements like the following:
Based on a comment of Robin Hanson’s: “I wonder if one could describe in enough detail a fictional story of an alternative reality, a reality that our ancestors could not distinguish from the truth, in order to make it very clear how surprising the truth turned out to be.”1
1Source: http://lesswrong.com/lw/j0/making_history_available/ewg.