Conversion bafflement

Not being a religious person, perhaps I lack the necessary basis for understanding and judging the religious beliefs of others. However, this is utterly baffling to me: the phenomenon of people who convert to a religion for political reasons.

Now I don't mean people who convert solely for political reasons in some cold and calculating way - the atheist who wants to have a chance at electoral success becoming born again, even if it's only superficial. I am thinking of people who are drawn to a particular faith because they agree with the political stances of that church.

I can understand leaving your current faith for one that also subscribes to the important religious dogma and principles you hold, if your present congregation or sect takes a stand you find objectionable (my grandparents quit attending the Episcopal Church when they began ordaining women, for example). But to join a church that has radically different religious beliefs which you do not yourself possess at present but presumably will convince yourself to adopt later, by whatever strange self-hypnosis you can manage, on the basis of sympathy with the church's political stances (abortion, or social justice, for example) is just utterly amazing to me.

Are people so adept at changing their religious beliefs that they are more willing to convince themselves that bread turns to flesh, that angels appeared to Mohammed or Joseph Smith, or that a certain tribe is the chosen people than they are willing to reconsider their stances on public policy issues? Does no one else see a fundamental disconnect here? How genuine is the belief in this case and how does one manage to blind one's self to the fact that your are only accepting their dogma because they also provide you with political fellowship?

UPDATE: Waddling Thunder muses about marriage conversions, a similarly puzzling phenomenon.
UPDATE II: Lewis has an example of political conversions from across the pond.