It doesn't

Or at least not what I had hoped for. I thought that it was similar to the Vikings in VI converting to christianity when their regions had enough christian believers. This allowed the Vikings to build churches (right?).

In BI you can do whatever you want, build the christian part of the techtree in one region and the pagan part in the other. The official religion of the faction leader or the settlement has no effect on what can be build. It only affects unrest and that is a missed opportunity IMO.