I was looking over at this "what should I do with my prophets" question, and realized that I couldn't give good advice because I wasn't sure whether you could prevent another civilization from starting a religion. After all, if you can use your second Great Prophet to convert enough cities that the AI just says "eh, looks like I'm religious already, this'll do," then it makes converting your enemies a much higher priority than enhancing your own religion. And since a given civ's religion is "whatever 50% of my people believe," a civilization might decide that they don't want to change "their own" religion by founding a new one.
So, if you convert an AI opponent's cities before they found a religion, will they give up on founding their own religion? Or will they found a religion anyway and try to spread the good word to their own cities? Does it matter which AI it is?
Best Answer
I noticed that if you convert AI cities to your religion, they still try to found their own religion. If your religious pressure is really high tho the AI religion has a really tough stand and probably won't be any danger to your own. I have also noticed in a few games that the AI still tries to spread their religion even when your religion is dominant.
So my answer would be "No you cannot stop the AI from founding a religion" But if you have a broad base for your religion even in their cities that is not really a big problem.