I just got my culture-specific relgious buildings working and I just had to share 
There are 4:
The stats may look underwhelming, but I plan to change the Theocracy policy to give +1
for Temple and +2
for the "Cathedral". Thought about making it +30%
but that may be overpowerd, even with 6 trees required for cultural victory. Also in the screenshot you see the Hanseatic League, available with Guilds. This just replaces the National Treasury (Wall Street remains in the game).

There are 4:
- Cathedral: Greco/Roman and European
- Mosque: Middle Eastern
- Pagoda: Asian
- Step Pyramid: American
The stats may look underwhelming, but I plan to change the Theocracy policy to give +1
for Temple and +2
for the "Cathedral". Thought about making it +30%
but that may be overpowerd, even with 6 trees required for cultural victory. Also in the screenshot you see the Hanseatic League, available with Guilds. This just replaces the National Treasury (Wall Street remains in the game).
Sorry.
(vertical growth bonus removed)
per 3
, +1
(health)
It can be fine initially, but cities will often get bonus culture for no reason, sometimes very big amounts. So as a fix the Sistine Chapel now provides 1
with Combustion