The five idiotic things (most of) the Left believes:

1) That communism can work, just that no one has yet done it correctly.

2) That there are absolutely no identifiable racial genetic differences, even when this harms people medically (diabetes, heart disease, etc. all  have racial genetic differing etiologies).

3) That absolutely no human evolution occurred above the neck.

4) That spewing more data at people is likely to change their minds.

5) That cultural relativism applied outside of an academic setting has any real value, or leads to greater freedom.

This is harder, because there are so, so many idiotic things the right (and in this I am including Libertarians) accepts as doctrine, but here are five idiotic things (most of) the Right believes:

1) That evolution did not occur at all.

2) That profit/affluence determines someone’s moral worth (ends justify means outlook, essentially).

3) That beating/hurting/killing someone is likely to change anyone’s or any group’s mind.

4) That women are subhuman.

5) That markets are self-regulating, a natural occurrence, and if the government would just get out of the way, we’d have a laissez-faire renaissance of the antediluvian free market bonanza.

Note that often these aren’t explicitly-stated beliefs, as either they are too outré to be stated aloud or written down, or they are just the subconscious machinations of group id that lead to observed action. But nevertheless, this is a pretty good encapsulation – at least as a first draft – of the manias that drive both sides to do the things they do.