The material sciences have admitted limitations in regard to revealing much information about an immaterial God.
So is the pursuit of truth best served by omitting God from science altogether?
"...[W]e have a prior commitment to materialism...to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counterintuitive."
- Richard Lewontin
How objective would you judge this "freethinker" to be concerning immaterial possibilities such as God; and how committed would you say he is to following facts "wherever they might lead"?
"Religion is neither provable nor disprovable, so God has no place in scientific inquiry."
Here's where the word religion, though a useful term, carries a lot of negative baggage in my mind. Religion, in one sense, can be described as human activity that seeks to fill ones need for "God". In that sense, one is right in saying religion and its potential biases have no part in scientific inquiry.
Yet science cannot rule out the possibility that God's existence is a reality. To do so would run the risk of blinding science to certain possible truths or conclusions. If one's view of science is to find the truth wherever the facts may lead, then no potential conclusion can be barred from consideration.
Of course, we both realize that the Bible describes God as spirit, and that the material sciences deal with non-spirit; but the overarching concern is that of finding truth. I address that implication more here, here, and here (and probably twenty other places).
The Christian "religion" is absolutely dependent upon certain truths: Jesus walked the earth, Jesus was resurrected from death, God created the heavens, God created mankind, and more. To the extent that some evidence exists of these things, then God, at least as a potential conclusion, does have a part in scientific inquiry. If Christianity boasts to have a theory that successfully accounts for the world around us, why not put it to the test at least as far as such evidence allows? (See my ten chapters on origins for arguments both for and against doing just that.)
I say all this and can still agree with Kepler that it should not be the first course of a scientist to look towards the divine. (Even Joseph did not do that when he first heard Mary was pregnant with Jesus.) For God is as capable of working transparently as he is visibly.
The cosmological argument for God
On freedom of inquiry
The origin of man
The origin of the earth
The origin of the universe