Good question , to answer this you have to go back to the beginning of the rumor which is as I believe based off at least originally the stories coming from the Indian sub-continent of It’s successful conversion to Christianity. As often with a lot of information at this time it was from word of mouth and very difficult to verify So rumors could blow up from a small Christian minority in India to a full blown kingdom of god in India. However as time went on it’s possible that in the 1200s the resulting popularity of this myth could be based on the great Kahn himself who had slammed into the Muslim world killing millions of them and sending tons of refuges into the areas around the remnant crusader kingdom and giving them reason to believe that as they were giving gods justice to the Muslims on one side that the Great Prestor John who in some stories is immortal was giving it to them on the other side a hammer and anvil of religious fervor. They never had any solid reasons for them to believe it but put yourself in their situation if you had traveled across the world in a time where you that was unheard of and you had gotten there not to a holy war where you drove the Muslims off the field but instead often time sat outside the walls of your holy cities being held by infidels and dying of starvation dehydration and just the grind of a siege and then you heard of an incredible kingdoms and they are coming to retake the holy land with you wouldn’t that just give you hope it’s understandable entirely for them to believe it don’t you think? source a book about it another book of primary sources about the evolution of the myth