4) Assuming certain core beliefs they hold are beyond argument.
This is a rather advanced defense mechanism, which normally kicks in when the person is already engaged in an intelligent debate but is not yet prepared to admit defeat and accept their opponent's arguments (note that I do not advocate that every political discussion should be a conflict of egos, but sadly they often are, and when that happens this is a very useful stance to take).
People are prone to take it for granted that their (usually inherited or indoctrinated) ideas of, say, democracy, free market, personal freedom etc. are sacred. They're not. Democracy is a human construct just as much as communism is, and as such it is flawed and often used to do harm. But when attempting to bring up this point in a bid to convince someone that the liberties of entrepeneurs and corporations should be limited and regulated, the response one gets is often of righteous indignation.
If you get this response, you've lost. When people start treating their political ideologies as gospel, you're out of the realm of politics and into evangelism. Give it up and get another pint.