He makes his point about the separation of church and state in an argument about - yes! - marriage:
The Christian conception of marriage is one: the other is the quite different question - how far Christians, if they are voters or Members of Parliament, ought to try to force their views of marriage on the rest of the community by embodying them in the divorce laws. A great many people seem to think that if you are a Christian yourself you should try to make divorce difficult for every one. I do not think that. At least I know I should be very angry if the Mohammendans tried to prevent the rest of us from drinking wine.
My own view is that the Churches should frankly recognise that the majority of the British people are not Christians and, therefore, cannot be expected to live Christian lives. There ought to be two distinct kinds of marriage: one governed by the State with rules enforced on all citizens, and the other governed by the Church with rules enforced by her on her own members. The distinction ought be to quite sharp, so that a man know which couples are married in a Christian sense and which are not.
It's from "Mere Christianity." I should maybe point something out here about my own writing on the subject. I have always been very clear that I am in favor of civil equality in marriage. I am not at all sure that the religious sacrament of matrimony ought to be open to gay couples. My instinct, in fact, is that it should not. The Roman Catholic church's view of marriage is so linked to heterosexuality and procreation that including gay couples within the same sacrament might violate its theological meaning. I'm open to debate on this theologically. But I make the same distinction Lewis makes: the civil and the religious spheres are very distinct and we need to make the distinction "quite sharp". The great blasphemy of Christianism is that it wants to erase the boundary altogether.