Respectfully, I don't know that I agree with this. Science and spirituality don't necessarily disagree. It's just that there are some questions that science cannot answer. For example, the question of "what caused existence to occur at all". Or "what is the nature of subjective consciousness". Because the tools of science are within reality, or within consciousness. It's like trying to use your own eye to see your own retina without using a mirror. You can't.

But there is "evidence" for these questions, they just can't be measured scientifically. You can't scientifically "prove" your own consciousness. But you know that you are conscious none the less. You wouldn't be thinking if you weren't. Likewise you can't "prove" what happened before the Big Bang. But the "evidence" for it is reality itself, so something must have happened. ;)