In other words, the fact that a person believes in God doesn't necessarily mean he has to reject most of modern science.

Very true. Many surgeons, physicists, scientists, etc. firmly believe in God.

The problem occurs when the two are mixed. When one (just speaking generally) attempts to "prove" the existence of God is when things get dicey. "Proof" of God would actually invalidate religion. Proof would make God definable, delimited, and place God under the realm of the scientific method. God is about faith. (Same argument applies to so-called "scientific creationism".