Until the AI is fixed so it doesn't spam Apostles and Barbs surrounding your city by turn 15 this game is no longer fun nor should it be played. Only managable road block to religious spam is play on Islands but it only slows the onslaught. Last game Rome build 58, yes 58, Apostles and Missionaries.
A lot of times when the AI does this, it isn't using the units to spread religion that much. That's why they seem to build up sometimes, because the AI doesn't always use their spread ability and they just accumulate.
Try declaring war on the AI that does this. Build up some units first, and place them around your cities within reach of all the religious units. Units with more movement points, like horsemen, are best, but you can use whatever. Denounce the AI, then declare a formal war when it becomes available (I think 5 turns later), or if possible, declare a holy war against the AI under the casus belli option.
Once you declare war, just start mowing down those religious units. It's not an attack, so you can kill one with each move (hence why units with more movement points are better). It will reduce that religion's presence for each unit killed. (I don't know if the extra belief that says your religion's pressure never drops due to losses in theological combat prevents pressure drops from being run over by a horseman, but the AI doesn't seem to ever take this belief anyway).
The satisfaction from killing 50 missionaries and apostles is worth the pain of having a religious AI spam units at you. And if you can manage to get the right to declare a holy war (I don't know exactly what triggers it, but the AI has to convert your cities to some extent, and you may or may not have to ask it to stop first), you won't have much of a warmonger penalty.