Logic tells me God doesn't exist but my heart says otherwise.

[Mudhammam]

Your brain does all the feeling, too. Just because something isn't accessible at the conscious level, or isn't comprehensible as a logical argument, doesn't mean it isn't of the brain, or that it isn't something important to the human experience.

I'm not so sure what causes religious feelings. I'm not sure I can see the evolutionary value of having them. But certainly, they are a big part of the human experience (though not all would call them "religious"). Maybe if we could better understand what the brain is doing when we have religious feelings, we could figure out the evolutionary value, and turn a counterproductive superstitious impulse into a superpowerful subconscious assistant.

One of the problems with science and atheism is that feelings sometimes get disregarded as unimportant or unsignificant, in place of logic exclusively as a way of processing the world. To me, that's not a good thing.

While I sympathize and agree with your assessment to some extent, I also think you're not giving "science and atheism" (really? What's atheism have to do with science or understanding the evolutionary or practical role of emotion?) proper credit for approaching the very subject at hand far more appropriately than their unscientific (i.e. religious) counterparts. Research as to the the cause or role of "religious feelings" has undoubtedly received attention in a number of fields, such as psychology and neuroscience. I would suspect the evolutionary value of such shifts in consciousness, if any, is similar to the practical benefits any other emotional high that human beings frequently experience bestows, whether it be the joys of simple aesthetic pleasure that follow from artistic endeavors or the feeling of accomplishment that follows scientific breakthrough, and everything else in between. Even certain animals use "magic mushrooms" to pass the time; my felines love their catnip. Maybe it's just something to do, and (obviously) also proves to be pleasurable, or appears to enhance life, and gives us a sense of meaning or purpose--like anything can--that without which might cause some to grow apathetic towards the future (and such a predisposition might quickly be eliminated from the gene pool, or at least not thrive as much as others). In short, emotions are integral to every thought and action that proceeds from the mind. Why would religious feelings have any special role other than their obvious effects that religious followers regularly report: a sense of unity with the world, peace, security, freedom, etc. These are important emotions but do they depend on any specific creed about the metaphysics of the Universe as it relates to other-worlds? Of course not.