I think one possible strategy is to get people to start being rational about being in favor of things they already support (or being against things that they already disagree with). For example, if someone is anti-alt-med, but for political reasons rather than evidence-based reasons, get them to start listening to The Skeptic's Guide to the Universe or something similar.

Once they see that rationality can bolster things they already support, they may be more likely to see it as trustworthy, and a valid motivation to "update" when it later conflicts with some of their other beliefs.