At least part of it, I think, is a misunderstanding of religion, and what it is. Religions do not claim to be irrational (who would?). Instead, they claim to be super-rational--that is, to have revelation of that noumenal realm beyond our understanding. Whether from the Earth Goddess or the Holy Ghost or the entrails of birds (I equate these only in their claims, not their veracity), religion claims to have information that would not otherwise be available.
I'm rather sympathetic to this claim. Any system of morality must come from beyond experience. Experience can only tell us what people do, not what they ought to do. To put it another way, let's examine the Free Rider problem, in my imaginary Greek city-state, Oinopolis.
Oinopolis must defend itself against the Persians, who are trying to impose a despotic, and more importantly, tee-totalling, rule over them. The Oinopolitans muster their citizens, and march out to battle. Despite the cowardice of a tenth of them, who run off to their homes, leaving the battlefield, the Oinopolitans triumph.
Now, judging from this data, we can see that both courage and cowardice are successful survival strategies (although I've simplified things by leaving out the likely reactions of the ladies of Oinopolis to those who took to their heels). We can favor neither one nor the other--we can offer no advice to an individual who wants to know whether or not he should stand and fight. He himself is better off fleeing, as long as enough others stay the course, and he can maximize his personal chances by running away. From an empirical point of view, we can commend neither the courageous or the cowardly, but only state the percentages in which we find them. To commend courage demands recourse to non-empirical sources.
But I digress.
Religion has rather fallen from favor of late, due to the opposition of certain groups to the theory of evolution. I don't see the conflict, myself, outside of this sphere, but it has been caricatured as "Religion vs. Science". Science is rational, falsifiable, empirical, and practical, in this view; religion is everything else. Of course a person coming to the debate with such preconceptions would label their opponents' position "religion", despite its lack of the true core of such beliefs.
The Ptolemaic system is not a religion, even if its proponents cling to it in the face of a better system (not Copernicus'! Eight minutes of arc, remember!). The Aristotelians are not following a religion when they persecute Galileo. Environmentalists are not religious when they claim data which do not fit their scheme to be false or irrelevant. They are defending an obsolete hypothesis. Religion is not about hypotheses. It is, truly or falsely, about revelation.