You're right to associate the two. The paper originally started because the founder of Christian Science, Mary Baker Eddy, was originally being hounded left and right by churches and other traditional institutions for her offshoot of Christianity. One of the avenues that this happened was through newspapers. This was pretty common at the time and pretty shameful. So she created The Christian Science Monitor as a result, not necessarily to push her religion, but because she wanted some fair press somewhere.

The paper itself is secular and has been known to put out some pretty compelling reporting from time to time. It was especially well regarded during the '60s and '70s when our country was going through a rough political time.

Edit: I used to read them a lot back in the early 2000s. I don't quite remember why I stopped, it was probably one of those things where I just didn't keep on reading them. I think I might add them back into my news rotation.

Edit 2: Apparently even Mark Twain got aboard the anti-Eddy train. Is there anyone in his lifetime he didn't pick a fight with?