The reason why these topics get so sensitive is that we transfer our discussion of the issues, which can be difficult, to a discussion of the people who hold the positions in question, which is easier. It is easier to talk about Democrats than it is to talk about Democratic policies, it is easier to talk about believers (or unbelievers) rather than beliefs. But when people take this "easier" path, we find that the conversation takes on a personal tone that is missing when we just talk about the issues. It is easier to say "Atheists just don't want to believe in God" or "religion is a crutch" instead of seriously considering the reasons why one should, or should not believe in God. But to say that religion is a crutch, or to say that atheists just don't want to acknowledge God, is to go beyond saying that the other side's belief is false to actually insulting the person on the opposing side.
If we could all learn to avoid what in logic is called the ad hominem fallacy, we could discussion politics and religion at the dinner table without raising the hair on the back of anyone's neck.