Most people don't use their minds for much anyway, which is why there is so much religion in the world.
OK, that's probably a little harsh - there are some reasonable religions around; there's... um...
Mind is no barrier to spirituality although I'd agree it is to Religion. Can't go being an earnest true believer and letting others do your thinking for you if you train and use your mind.
BUt let's not confuse the issue here - we are a sick society, one that has a wrong concept entirely about being only body and brain, where our development is seen as random chance and to have no higher purpose. Even of those not mired in the excesses and deadening effects of Religion, Mind is not necessarily being used well.
Mind, developed and tuned, is an excellent tool for all our purposes, including Religion. It's possible our entire point of being here at all is tied to learning to use our Mind, to discovering the processes that allow us to focus or go out of focus at appropriate times.
Mind IS a wall between Man and God - if by God you mean the limited and psychopathic God put forward by Religion. But to accept such a statement as some kind of truth without any modifiers shows a mind not working, and the desire to learn truths from others, which is exactly what the God in CWG (another set of truths accepted by the OP) says is a wrong way to live.
But Believers are full of such contradictions
Use of an active and trained Mind might have pointed that out before posting and showing a lack of comprehension of the issue.
And to clarify, as I have said before, the issue is NOT Faith. The major Religions like to make faith equal to belief but they are different things. Faith is a higher order event and it allows modification as facts come along. Belief alters reality to fit the belief, even to the extreme where the rabid believer literally does not see facts. The two words are not interchangeable.