Cognitive biases abound on both ends of the political spectrum. Recently a test of UK MPs showed they can't do basic probability, let alone deal with the kind of biases we discuss here on LessWrong. In the US, compare global climate change denial on one end of the spectrum with GM scares on the other. At first glance, neither group seems more likely to be susceptible to bias than the other.
For reference, I vote mostly with the Green party in the US, despite their idiotic views in homeopathy, pseudoscience, nuclear power, and several other talking points. There is no such thing as a Technical Rationality Party, and even if there was, I'm unsure as to what positions it would take on several issues that differ greatly on ethical assumptions (and hence bayesian priors).
For example, I'm sure most of you eat meat because you value the feelings of nonhuman animals so much less than I do. As a vegan, my ethical assumption is that there is nothing special about humans that makes their preferences matter more, and so I compare the benefit of good taste against the suffering involved with factory farms, concluding that it is not ethical for me to eat meat. Yet I completely understand and accept that several LessWrong members will think there is nothing wrong with eating meat, and will not be suffering from bias in coming to that conclusion, merely because they go into the bayesian calculation with a completely different prior: they qualitatively prefer humans rather than quantitatively, like I do.
Different ethical assumptions result in different political positions, even when no bias is present. Since ethics is not something that is an independent part of the world but rather is a part of what we impart into it, there is no basis on which any of us can conclusively convince another to change their initial ethical assumptions, except by exposing that one's current view is inconsistent or flawed in some way. Yet there is a huge gulf between being able to say "your ethical view is inconsistent with logic" and "my ethical view is the preferred one". Just because they're wrong doesn't make you right.
This is completely unrelated to your main point, but for the record eating meat isn't mutually exclusive with regard to the feelings of animals. I personally don't feel that my diet has enough of an impact on food production to warrant the inconvenience and discomfort that would come with a vegan lifestyle.
Just a thought I had the other day; what do you think that the political ideas of conservatism have to do with cognitive bias? I mean, how much are people willing to change naturally, without arguing any points?
I know very little about all of these things, so forgive me if this is a silly thought.