It’s generally the more conservative, even fundamentalist, versions of religions that strenuously evangelize and seek converts.
So, other than bringing up children in the faith, how do more liberal religions reproduce themselves? I imagine there’s a good deal of stealing from more conservative movements. For example, a college student can come to think scriptural literalism is unworkable, and drift toward a less rigorous version of her childhood faith. There has to be some amount of conversions from nonbelieving circles as well; there has to be something to the stereotype of nonbelievers coming to look for some more spirituality in their lives.
But still, the question is interesting. Since liberal religions have the reputation, supported by the sociologists, of not holding onto their own members that well (partly because they aren’t demanding enough), to reproduce, they need a stream of converts. Where do they come from? Disaffected conservatives? The previously only culturally religious or religiously indifferent, who come to think they need more church or mosque in their lives? And is this enough to keep them going?
I should really talk to a sociologist of religion about this.