As part of our governmental setup, we are supposed to have "separation of Church and State". Therefore, the subject of religion should not be a part of political campaigns. Religion is a personal belief system and should be left as such, for each individual to believe as he or she chooses without political influence.
It is not democratic to ban religion from political campaigns. Part of the Greek origins of the word "democratic" is including all of the people in a given place. And people inherently will have their own religious views and opinions as they will have their own political opinions. It is however more politically safe to leave religion out because then you can appeal to people across religious divides.
While religion permeates our political process in many unfortunate ways, affecting policy and blinding outlook, it would be undemocratic to ban it from being in the political arena at all. Religion, right or wrong, is still a big part of the lives of many people, and to bar it from campaigns is going too far.
It is important to let the public vote on issues that matter. Often times, when a person knows a candidate's religion, they can guess how the person is going to vote on certain issues. Often times, people want to vote for a candidate that will take a certain position on religion liberties. This should be allowed.