In this case, a Great Prophet would work better than a Missionary, for their Conversion strength would only turn over a couple Citizens, while a Great Prophet could turn the Holy City and make its majority religion change, even permanently - but it'll still be a Holy City with a few followers, as they will gradually return due to the Holy City base of +30 Pressure.
It would seem that their cumulative Pressure over time may come into play - a case in point being a Holy City that has long held its position but recently finds itself surrounded with other Cities giving Pressure - the Citizenry will not fall to the new ways so quickly because there has been so much pressure exerted there in the past. With multiple Religions competing, it will take even more to turn them over, although with more Pressure you are guaranteed to eventually win the majority.
Without any other Religion competing, it takes 100 Pressure to convert 1 Citizen to follow a Religion. Cities that are nearby and have converted will return pressure, giving you a higher value in the Holy City and making it very hard to Convert naturally. Holy Cities exert 5x this amount of Pressure on themselves, so 30 Pressure per turn. So, if one City were feeling pressure from 3 Cities within that 10-tile range, it would be getting +18 Pressure and convert a Citizen roughly every 6 turns. Religious Pressure varies by game speed, being much lower on slower speeds like Marathon, so all numbers here are for base. Each Religious City will send out +6 pressure for its Religion to all Cities within a 10-tile range. Religious Pressure is generated by Cities that have converted to that Religion and are Religious. If a Religion has converted at least half the Citizenry, a City becomes Religious and gets that Religion's benefits. Spreading Religion Naturally - Religious Pressure Civilization 5 Religion Guide Converting Citizens and Religious Pressure in G&K and BNW Civ 5 Religion Guide - Gods & Kings and Brave New WorldĬities get Religious Pressure from Trade Routes and Cities within 10 Tiles
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