Hi, "now faith."
It's been awhile since you wrote your post and Ive been away from the forum for much of the time, so my apologies for the delay, but I owe you my reply. Yes, Christ is mentioned all the time and Masonic ritual leans heavily on the Bible.
What you are referring to as a rule of a lack of affiliation does not exist. I know the churches that most of my brothers attend, and Masonry encourages members to be active in them, in fact, in whatever denomination is theirs. The rule is that all members must be believers in one God and that the human soul is immortal.
If you are a Baptist or an Episcopalian or even a Catholic (the church formally opposes Masonry, as you probably know), it is all the same to the lodge, and I know Masons who belong to all of these plus, of course, other examples that might be mentioned too.
There is no Masonic god and there is no effort to have members agree that all religions are equally good, or anything like that, although there are many people who have heard gossip that says Masons believe in both of those things. It is not so.
Thanks for asking your questions.