Charlotte Mason is a teaching philosophy, rather than a specific curriculum, so you can integrate religion to whatever extent and in whatever manner you desire. I'm sure there are those who would argue with that statement and say that the structure of the philosophy inherently integrates Christian values or something, but the fact is that you're free to choose which books you read, and free to integrate religious material (or not) of whatever sort you feel are appropriate for your family.
There's a relatively recent thread on here about a Pagan curriculum, and several of the participants seem interested in something CM-style.
We use
Ambleside Online in a secular manner by simply leaving out or substituting for blatantly religious material. For example, in Year 1, we leave out the Bible, Trials and Triumph, and Parables of Nature. Next year, we won't be doing Pilgrim's Progress (don't know if we'd be doing that one even if I was Christian - I was bored out of my skull by a cartoon version when I was in Sunday School as a kid). We also integrate books and resources from other CM and classical sites, secular or otherwise, as well as things I come up with myself. I like AO because it's free and someone's already done so much of the brainwork for me, and I haven't found a similarly well organized, free, secular resource.
I do find that older books (and by that, I mean anything pre-1960s or so) often emphasize Christian values either overtly or covertly, and often assume a basic familiarity with Christianity. These books tend to be heavily utilized in CM-type curriculums, both due to content and quality. We read them anyways, because I don't believe in throwing the baby out with the bathwater, but it is something to be aware of.
