There's a few ways, mostly through events.
The most simple is that random-generated courtiers will have the religion and culture of their home courts capital, so if someone converts one pecheneg pagan province to pecheneg orthodox, more orthodox courtiers will start appearing. Courtiers at christian courts may also get converted in events (but most die in the process, since it's the inquisitors doing the converting...).
Any children in church education will switch to the religion of the highest-ranking lord (King if there is one) in the realm when they graduate, so if the heir of some ruler is being fostered elsewhere, that's a way for a branch of a dynasty to switch religion. In DVIP I think children always graduate from church education before they go home, so you can switch your dynastys religion at will, actually, provided you can get some orthodox realm (or whatever) to accept fosterlings.
Vassals can get an event asking them to convert. Force-vassalising pagans/muslims and them getting this event is probably the easiest way to get characters to convert. Any children they have at their own court in church education will convert for sure eventually.
The last one is the most common, and it's what i'm betting on, at least in the case of Lt. Tylers game. An active crusader king will end up with arab catholic or orthodox characters marrying and reproducing over their respective portion of christendom (I have an arab catholic duke in Sweden).