When I referred to "personal intuitions" I meant controversial or arbitrary-sounding personal intuitions, such as "I feel there's a god" or "I feel abortion is immoral" and then using those intuitions not as some sort of evidence but as priors.

I think most people just hold things like faith and emotions higher than logic and probability. Asking, say "how do you know that murder is wrong?" would, I imagine, freak out some people who aren't philosophers. The whole idea that belief in god is a matter of probability is not held by many people, and moreso with moral questions. Most people, including intelleginet, educated people, do not seem to think that any justification for political opinions is needed except 'anyone who disagrees with me is evil/stupid'.

Its actually worse than this - there are people who are deeply uncomfortable with having a notion of truth at all, because if there is a notion of truth, then some people are right and some people are wrong, and the idea that people might be wrong about something is offensive.