Making the extra production a building XML tag or even just a variable in GlobalDefines would've been more intuitive to me. Well, the effect is tied to the membership rules, lost after defying a resolution ... And I suppose one could introduce additional religion-based voting bodies. Actually, Civ4VoteSourceInfos.xml didn't even exist before the BtS expansion. It seems that a free specialist (FreeSpecialist tag) had been considered, perhaps tested, as a (first?) alternative. If a free Priest in all loyal cities had been the initial idea, this might explain why, oddly, the Apostolic Palace itself adds no Priest specialist slots. (The Shrine, in contrast, adds 3, but more Priests aren't usually needed once the Shrine is built.) The Civic tag btw causes a particular civic to be required for full membership.
It looks like the ReligionYields, as the tag name suggests, do nothing when the vote source isn't tied to a religion. The logic for that is in CvCity::processVoteSourceBonus. Well, these things should be easy enough to test. By the voting having switched to the UN, I guess you mean when the AP wonder has gone obsolete. Because the AP and UN can coexist as active vote sources when different players construct the respective wonders, and iirc this comes down to obsolescence. (If it's the same player constructing both, then Mass Media will have obsoleted the AP wonder.) So maybe changing/ removing the ObsoleteTech would accomplish what you want. Though, if you want the voting to stop earlier than the ReligionYields, that could be difficult.
