Hi achristian -
I think one of Mere Christianity's greatest strengths is that it does exactly what it sets out to do: make a case for "mere" Christianity by stepping back and seeing the Church as a whole, by being inclusive, by putting all the nitpicky divisiveness on hold for a moment. That is why it touched me (a Catholic) as much as, I am sure, a broad spectrum of other Christians. We all share our faith in Jesus Christ (even Catholics!). Also, his audience is really non-Christian; it is therefore strategically better for an argument to not meddle with the differences which divide us before making a case for 'basic' Christianity. I may be wrong here, or oversimplifying... but whatever tradition Lewis as an individual belonged to is beside the point. He made a case for Christianity, and has brought a great many people closer to Christ (people did not grow up Christian, people who had strayed or become disillusioned, people who thought it was bunk). Let's keep keep this in perspective.