What is rational?

The so-called “scientific atheists” claim that while science is rational, religious thinking is irrational (seemingly oblivious to the cogency of, for example, McGrath’s reasoning), but what do they mean by “rational”? Do they mean that our beliefs must cohere with each other and be proportioned according to the evidence? But empirical data has to be interpreted according to an existing system of beliefs, and that system can be modified catastrophically (in the mathematical sense) in the light of new evidence.
......Even within science, scientific paradigms change. And catastrophic modifications must be occurring in the minds of individual scientists as they grow up; presumably they do not fixate irrationally upon the first system of beliefs that they acquired. Indeed, similar modifications are probably occurring for all of us, a lot of the time, and so the coherence of our beliefs would seem to be more of an ideal than an actual possibility.
......Furthermore, in order for our beliefs to be realistic, they should depend upon how the world is, but we judge the importance and likelihood of possible evidence in the light of our existing beliefs, so we are rather at the world's mercy when it comes to being rational. Although I’m not quite sure what “rational” means.

Imagine, for example, that Dawkins is abducted by aliens. Given such quantities of first-hand experiences, Dawkins would probably change his beliefs about UFOs. Had another man come to him earlier with such a story, Dawkins would surely have told him to take seriously the probability that he had imagined the abduction. And when Dawkins returns to Earth, and that empirical data turns into memories of a very strange character, he might naturally and not unreasonably revert to his original skeptical beliefs about UFOs (and regard the abduction as a dream). His friends would no doubt be pleased by his return to sanity.

Now, suppose that McGrath is shown all of the primary data and all of the reasoning that atheists find so important (suppose that he does not already know it), and suppose that that evidence is so good that he loses his faith, temporarily, but that he similarly reverts to his earlier beliefs eventually (and regards his loss of faith to have been the work of the devil). Scientific atheists would hardly say that that reversion was rational.

We can suppose that Dawkins and McGrath were both attempting, at key moments within those fictions, to choose between one set of beliefs (with their explanation of the data) and another set (with their explanation). Making such choices rationally is clearly consistent with being in two minds about things, from time to time. It is consistent with holding inconsistent beliefs, from time to time. And whilst those two examples are naturally rather odd, that was just to keep them simple. People who try to think things through will often find themselves in analogous but much more complicated situations, often with little rational expectation of making their minds up in any reasonable time. But in various situations, one set of beliefs might be more appropriate than another. Is such appropriateness more important than coherence, when it comes to being rational? And could such appropriateness be a big part of what “scientific atheists” mean by science being rational and religious thinking irrational?