Now just to the southwest of the previous picture, I did not get here early enough: Even though he spent tons of effort converting his cities to Buddhism, they all converted back to my religion due to passive pressure from all the surrounding cities. I got to his cities (and the surrounding ones) early, before he founded his own religion.
You want an interlocking grid of religious pressure, so that even when religions start popping up, they have difficulty spreading against the wall of cities already converted. Religious texts Religion spreads 34% faster (68% with Printing Press) Then you solidify that with one of the two Enhancer Beliefs that improve passive pressure Itinerant preachers Religion spreads to cities 30% further away You want to primarily target central cities that have many others within passive pressure range. So basically to become a dominant religion, get to a religion as fast as possible, and get missionaries out there ASAP.
Instead, you want to be the established religion that requires tremendous effort to dislodge. As Paralytic notes in the comments, spreading into an established religion requires tremendous effort that is often not worth it. The key to religious dominance is spreading early before other religions start popping up.