Claiming that science cannot explain consciousness is not "religious" or "irrational", it simply is going back to what science
is, namely, that "ideas are tested by experiment". Science as we understand it today cannot really explain consciousness, the same way it cannot really explain what it feels like to be a bat. It can explain how bat's use senses perceive environment using physical principles of sound transmission, but it can't convey what bats
feel when they perceive environment. Similarly, I cannot convey my internal conscious experiences to you. I can only try to describe them to make you interpret them in terms of your own conscious experiences, but I can never make you feel what I feel, or if I can, there's no way to tell that.
Of course, in future we might understand things like consciousness and qualia, and it's likely that people who do it will be scientists. It won't be "science" though as we understand it today, it will necessarily have to be something bigger. Let's call it "science+".
And, of course, just because science can't explain consciousness doesn't mean that religion can. It can certainly claim to be able to do it, but will be as convincing as the religion is at explaining everything else.