The belief itself can be removed by expelling or killing off the populations involved or by repressing it with favorable policies toward a majority faith. It isn't exterminated entirely but it is functionally removed from that society (see Spain with Muslims and Jews in the 15th century or Eastern Europe with Jews again in the 20th, or China's suppression of various religions under Mao, etc). I would argue most societies religious suppression of minority faiths is the norm, even including the US and Western Europe and even into modern day (see Mormons and atheists, among others. Scientology for example is outright banned in some countries). That doesn't mean these minority faiths and beliefs will disappear and cease to exist, or that they won't eventually flourish in the new environment anyway, but it does suggest that the social norm is to suppress and restrict new faiths and the people who practice them in favor of the local majority.
I think the existing system of "the majority local faith in a city governs any applicable beliefs that the city uses" works fine without needing new layers. I might also prefer a watered down version of many beliefs practiced locally, but I think that reduces the importance of founding faiths and pantheons and reduces their power and effect individually. It would be more realistic, but would reduce some game play options too much without much benefit. I think we should have to do at least some strategic decisions relating to faith (which one goes where, what city we need to defend, etc) rather than totally passive acceptance of whatever comes our way when a religion spreads and where.
I think the existing system of "the majority local faith in a city governs any applicable beliefs that the city uses" works fine without needing new layers. I might also prefer a watered down version of many beliefs practiced locally, but I think that reduces the importance of founding faiths and pantheons and reduces their power and effect individually. It would be more realistic, but would reduce some game play options too much without much benefit. I think we should have to do at least some strategic decisions relating to faith (which one goes where, what city we need to defend, etc) rather than totally passive acceptance of whatever comes our way when a religion spreads and where.