I agree with @nwrickert in that compartmentalization is similar to how we normally live out our lives. My preference to use a different term is more because often “compartmentalization” has the connotation of tension, conflict, or contradiction, which was the feel that I got from @John_Harshman when he used that term. (Again, maybe I’m reading him wrongly.)
Secondly, compartmentalization also seems to point towards an unwillingness to wade in the waters where religious and scientific methodology do seem to be in tension, such miracle claims or whether God answers our prayers and how God acts in the world.
Finally, from a Christian perspective, I also find compartmentalization personally inadequate to live out 1 Corinthians 10:31: “So whether you eat or drink or whatever you do, do it all for the glory of God.” How do we do science for the glory of God? (Of course assuming, in my case, that I’m not sympathetic to ID or creationism or the like.) It seems harder to understand how this is to work if religion and science are separated off from each other.
For me, resolving the two is really important. It’s certainly a work in progress for me, not something that I have all the answers to right now.