FenrisWolf456
Chieftain
Well ... yes ... but we were discussing your Religious Alliance with your neighbour ... Alliances are a rather modern concept and a mid-game mechanic. I imagine it has a similar effect as Cultural in that your religious pressure doesn't affect your alliance partner (though I don't actually know, I mostly just form a religious alliance for the bonuses to having an alliance such as policy cards). As well, your partner is likely to not actively attempt to convert your cities.
And the 'slave religions' are already considered in the game, as the followers of other religions in your otherwise dominated cities. Which then become the tolerated religions in our more modern ideas of religious freedom.
Then why are you questioning the AI getting upset at you converting one of its cities? The AI will clearly want their religion dominant, to the point that they rabidly send out missionaries and apostles to any city that at least doesn't have a majority religion. They do seem more hesitant to attempt converting cities of other religions, however. I often see apostle trains go through my territories but never attempt to convert my cities if they have a religion already. Though I have also seen pitched apostle battles of rival civs around my cities when I don't discover my own. There seems to be a trigger in the AI where they won't attempt direct conversions of cities if you have established a religion, but you're open game otherwise. Perhaps it depends on how much they like you, since conversion is seen as a provocation much the same as spies are. In a way, I wouldn't mind more aggressive religious converting, but then I remember the high levels of annoyance with that in Civ V, so I'm not sure which I'd rather have.
But there are mid/late game mechanics in place to promote religious warfare, or at least the effect thereof. The Holy War casus belli, for a start, as well as the World Congress vote where you can allow everyone to squash a particular religion's religious units.
As to why the AI wasn't trying to get the converted city back right away, likely just the quirk of the AI coding. It seems to me that the AI often gets locked into a particular action, such as really wanting to convert some city state on the opposite side of your empire, and will send its stream of missionaries/apostles to ensure it gets it, fighting endlessly with other religions to do so.
I remember one game in which I baited Dutch apostles to a nearby city state so that my Debaters could demolish them, thereby convincing Wilhemina to send more (also showing the absence of any attempt to convert my actual cities). Or another game where I began questioning why I was bothering converting a city state, knowing full well that the Aztecs would come a-running ... and lo, a few turns later, there came the horde of blue missionaries out of the fog of war.
So it could have just been the AI locked into an action to its detriment. Or perhaps it calculated that religious pressure would eventually bring its city back into the fold. Or perhaps the benefits it was receiving from the rival religion were enough to convince the AI to not bother with re-converting.
But in any case, as said before; AI sees one of its cities converted to a different religion that its own, from a civ that effectively promised not to do that, so it triggers a 'Stop that' response to you.
