Christianity is based on principles otherwise rationally believed true,
Oh? I think I disagree. If you can actually name those principles and justify them,.... well, let's just say that others before you have tried and failed.
so that definition doesn't seem to work without applying circular logic (that belief in Christianity is based on irrational principles which are irrational because they are based on other irrational principles).
I think I'm asking what defines a principle as being "rationally" believed true.
No, I think I'm willing to stand (informally) behind what I wrote.
There are lots of reasons for believing something that aren't "rational." For example, "believe me or I'll hit you with a big stick" (formally known as argumentem ad baculum). Similarly, "appeal to pity" or "appeal to consequences" (I'll save the pretentious Latin) are not rational reasons for believing in something. In general, a principle is "rationally" believed in if there is legitimate evidence/reason to support it -- but "evidence" here is taken in a much broader sense than simple empiricism.
For example, Paley's argument from design -- "A watch-implies a watch-maker, therefore a universe implies a universe-maker" was quite rational in the early 1800s, and still has some force today. However, to step from this universe-maker to the Christian God was never warranted, even then.
Most Christians probably have reasons to believe, although likely not reason enough for you or I to believe. However, the fact that one might rationally not be convinced by the reasons held for belief that intelligent life exists elsewhere in the galaxy doesn't make such a belief irrational.
Of course not. We can "rationally" hold differing beliefs, depending upon our assessment of the degree of support offered by a particular set of evidence, or the credibility of the necessary theoretical scenario to support it. If you tell me that the reason you missed the final is because your car broke down on the way in to campus -- well, I might "rationally" disregard that statement because I've been told that particular lie so many times in the past years of teaching. It lacks credibility (to me), while my first-year colleague down the hall might buy it, either because he's naive or because his experiences with students involved more truthful ones.
However, just because someone has "reasons to believe" doesn't mean they're rational reasons. Pascal's wager, for example, is not a rational reason to believe (despite the fact that it's often presented as one in the apologetics literature), but an elaborate example of the "appeal to consequences" fallacy.