Lots of things can be taken on faith without straying into the darkness of irrationality. As I wrote previously, some hard-core atheists, acting like the appointed guardians of the term "rational," insist that everything other than acceptance of evidence-based concepts represents irrationality. But I think it is meaningless as well as unfair to use the same term, laden with pejorative connotations about mental fitness, to describe belief in things that are possible but unproven and belief in things that are impossible. Indeed, belief in things that are shown to be factually false or logically self-contradictory is irrational (specifically, delusional), but I will not apply the same term to belief in things that, if not proven true, have at least not been proven false.
Thus, it is irrational to believe that God literally planted a fully formed human male on a planet then just 6 days old, a few thousand years ago -- a literal interpretation of this religious tale conflicts directly with incontrovertible geological evidence relating to the age of the Earth. But if we accept the geological time-frame, I can propose at least 3 scenarios to explain the origin of life on Earth: (1) random reactions between organic molecules in the primordial oceans resulted in the spontaneous formation of a self-sustaining object exhibiting the processes we associate with living things; (2) life arrived on Earth in the form of spores from space, as proposed by the 19th century chemist Svante Arrhenius; and (3) God created a microorganism and then allowed it to evolve and diversify over the ensuing eons. All of these scenarios lie in the realm of the possible -- that which has not been proved or disproved. They are not supported by evidence, yet they are not irrational in the sense that young-Earth creationism is irrational. Lacking proof that something is true is not the same as having proof that it is false.
At this point, atheists may invoke Occam's Razor, the logical principle that says, in essence, that among contrasting explanations for some phenomenon, the one requiring the fewest unsubstantiated assumptions should take precedence over all others. And of the 3 origin-of-life scenarios outlined above, the last requires the assumption that there is a god, and therefore should be rejected. Maybe, maybe not. All 3 require great assumptions -- that conditions in the primordial oceans were really that favorable to the spontaneous emergence of life, and that spores from some other world reached Earth and found a hospitable environment (and we won't even ask how life emerged on the Planet of the Spores). Moreover, the logic behind following the Razor applies mainly when there is something at stake in the decision; what is at stake in a question whose answer can never be known?
So what does rational faith look like? Belief in things that are possible; non-delusional belief.
By the way -- I have no argument with atheism. Belief is a personal matter; what counts is how we act in this world, and most of the atheists I know are at least as decent human beings as the religious people I know.