Hey there,
That's either a Rome: Total War mechanic no longer relevant in Med2 or an urban legend. Only buildings in mods/ebii/data/export_descr_buildings.txt that say something like this are doing any culture (aka religion) conversion:
Code:
religion_level bonus 1 requires factions { f_sauromatae, } and not region_religion rel_b 30 and event_counter ecReligionUpdate 1
There's no reason to smash markets or temples or anything just because they have a different faction of origin, unless the artwork for it is really bothering you and you have money and build time to spare. But when they upgrade to the next level, they'll start using your artwork.
Buildings that convert are going to be things like trade colonies, settler/raiding colonies, Hellenic colonies and to some extent poleis (to maintain a certain minimum), Native military colonies, Nomad enclaves, and stuff like that. Basically whatever is the conversion mechanism for each faction, plus as you see only certain factions unlock some of the conversion bonuses. To avoid digging into the files, every 3rd turn or so it's a culture conversion pulse. Just keep trying to right click on a known conversion building from my list here, and within 3 turns you'll see it mention "Culture Conversion" (unless of course you are already outside of its range; e.g. the one I linked above stops updating rel_b once rel_b is at 30%), and you should see the "Cultural Conversion" item on the building summary that you usually don't see. Then you can check out all your other buildings if you're wondering which are converting on this pulse.