I have long thought the many of the members of the cult of militant anti-religionists — people like Richard Dawkins and Christopher Hitchens — have been assailing a straw-man.   Their target is religious belief of a particularly narrow, fundamentalist kind, and as Terry Eagleton among others have noted, this target is a gross caricature of most of the people who practice or believe religious ideas.   The main argument of the anti-God cult is usually that religious beliefs are held without evidence.
First, as the writer Karen Armstrong discusses today, for most people, religion is about doing, not about knowing.   It’s really only philosophers and their street-brawling imitators who obsess over beliefs.   Indeed, because doubt and scepticism are integral parts of most of the world’s religions, religious practice may not necessarily start with belief, but in fact end with it:  Belief can be what comes after you practice spiritual exercises long enough, not necessarily what causes you to practice them. People do zazen or yoga not because they are already enlightened, but to achieve enlightenment.
Second, the issue of evidence is problematic in these diatribes against religion.   It is simply not the case that there is no evidence for religious or spiritual ideas, or that such ideas are only supported by the irrational or the feeble-minded.   Most people who proclaim any adherence to religious or spiritual ideas will assert they have evidence for a realm beyond or outside the material world.   This evidence is usually of the form of direct personal contact with a spirit world or with spiritual entities, as for example, in the experience of Janet Soskice or the physicist Oliver Lodge.  Anyone who has spent any extended period in Africa or in East Asia will know people — sober, rational, and intelligent — who have had, and continue to have, what they experience as direct contact and interaction with spiritual entities.
Of course, such direct, personal evidence is usually not replicable at will, nor observable to others.  That makes it invalid as the basis of science, which is a shared undertaking, but does not make it invalid as evidence for personal beliefs or actions.   Knowledge of the existence of things unseen can be obtained by merely being in the presence of such entities, as the Sufi philosopher and founder of Illuminationism, Shahab al-Din Suhrawardi (1155-1191) argued in the 12th century. Knowledge-from-being-in-the-presence-of is a valid form of knowing, just as knowledge-from-tasting is.  Our subjective personal tastes in food and drink, say, or our subjective experience of being in love, are also not observable to others, but that does not invalidate them as evidence for our beliefs or as a rational basis for our actions.    When I say I prefer coffee to tea, this is an inference based (usually) on my personal, subjective reactions to the tastes of the two different liquids.  Only I know whether this inference is based on true reactions or not; if I am a sufficiently-clever actor, no one will ever be able to conclude anything about my reactions to the respective tastes other than what I claim.
It may be that experiences understood subjectively as contact with spiritual entities can be replicated in the laboratory by stimulating particular parts of the brain, as recent experiments appear to show.  But it does not follow from such research that all religious experiences are due to similar mental stimulation, just as using implanted electrodes to create the subjective experience of the taste of coffee would not thus imply the non-existence of coffee.
In closing then, I wonder which is more rational:  to commit to certain religious beliefs (or undertake a spiritual practice) based on one’s personal subjective experiences with the divine OR to devote one’s career to studying mathematical models of additional space-time dimensions, dimensions for which  there is as yet no evidence whatsoever, not even any subjective personal experience?  If Dawkings and Hitchens were really worried about irrational beliefs, they should be attacking the practitioners of String Theory and M-Theory.
References:
Mehdi Amin Razavi [1996]: Suhrawardi and the School of Illumination.  London, UK:  Routledge.
POSTSCRIPT (2017-06-04): In a New Yorker profile of business author Clayton Christensen, he is quoted regarding his daily reading of The Book of Mormon:

One evening in October, 1975, as I sat in the chair and opened the book following my prayer, I felt a marvelous spirit come into the room and envelop my body. I had never before felt such an intense feeling of peace and love. I started to cry, and did not want to stop. I knew then, from a source of understanding more powerful than anything I had ever felt in my life, that the book I was holding in my hands was true.” (Page 90)

Larissa MacFarquhar [2012]: When Giants Fail. The New Yorker. 14 May 2012, pp.84-95.