I think first that it's impossible to apply any kind of logic to God without first making a bunch of provisos. Many religious people assert that the laws of logic only exist because God created them. Think about that for a second. This "God" exists beyond logic.
God has no place as explanation in science, because it doesn't explain anything. Why is the sky blue? That's the way God made it. Why does it look like organisms evolved on Earth? That's the way God made it. It "explains" any possible observation and therefore explains nothing.
Materialism is a sine qua non for real science.
Science can study people's ideas 'about' God, because ideas of God exist in people's heads.
Science can study religion, because religion exists in the collective of physical humans.
But science can't study any real supernatural phenomenon; nor even recognize their existence.
