If you believe in a God then you probably believe that God made the laws of science. Therefore there is no problem believing both religion and science. The problem is that much of science is made up by people who refuse to believe in God. They look for answers that do not involve God. Science should allow for the possibility of God. Then there would be no problem believing both religion and science.
I agree. Science does not
ipso facto preclude the existence of God. However a fundamental feature of the scientific method of enquiry into nature is methodological naturalism. This means in effect that the scientist only considers explanations due to natural phenomena, not supernatural phenomena. This was a basic advance in the approach to the study of nature, when modern science got started after the Renaissance, that has served it extremely well. It is just part of the science toolkit for analysing nature.
Some, perhaps many, but by no means all, modern scientists have extended methodological naturalism into a complete worldview: metaphysical naturalism or philosophical materialism, asserting that the physical, observable natural world is
all there is and therefore there is no God.
On the other hand many scientists do not extend naturalism in this way and are religious believers. There is no reason why they should not be.