Incorporating
@CrazyG 's suggestions:
For culture:
Ancient 2/4 (was 1/3)
Classical 3/8 (was 1/3)
Medieval 5/12 (was 4/10)
Renaissance 8/16 (was 4/10)
Industrial+ 12/26 (was 10/22)
Culture is buffed because it seems like there is decent consensus that it's weak currently.
For faith
Ancient 2/4 (was 3/6)
Classical 3/8 (was 5/10)
Medieval 5/12 (was 7/14)
Renaissance 8/16 (was 9/18)
Industrial+ 12/26 (was 12/24)
Faith is nerfed because it seems there is decent consensus that it's too strong currently.
For science:
Ancient 2/4 (was 1/4)
Classical 3/6 (was 2/6)
Medieval 4/10 (was 4/10)
Renaissance 6/14 (was 6/14)
Industrial+ 10/20 (was 10/20)
Slightly buffed early game, overall lower yields than culture/faith because of those free military units.
For gold:
Ancient 2/4 (was 1/3)
Classical 3/6 (was 1/4)
Medieval 4/10 (was 2/6)
Renaissance 6/14 (was 3/8)
Industrial+ 10/20 (was 4/10)
Slightly buffed early game and significantly buffed later game (where it is currently incredibly weak IMO). Overall lower yields than culture/faith because of the free happiness, equal yields to militaristic CSs. Still might be the weakest CS yield just because gold is usually worth less than science/culture but maybe the happiness makes up for it enough? I guess I could buy that happiness is stronger than free military units.
For food:
WAS:
Ancient/Classical/Medieval 3/6 (0.5 to secondary cities)
Renaissance+ 4/8 (1.5 to secondary cities)
NEW:
Ancient/Classical 3/6 (0.5 to secondary cities)
Medieval/Renaissance 4/8 (1.5 to secondary cities)
Industrial+ 5/10 (2.5 to secondary cities)
Slight buff in Medieval, buff in Industrial+.
I wouldn't be opposed to it but others seemed happy with the scaling stopping and letting CS importance be more about votes than yields in late game. In the interest of getting a consensus I figured I'd just leave that part be.
I certainly had Siam in the back of my mind when proposing these changes, as the ancient/classical yields from CSs become glaringly apparent with him. I think the above changes would make his game feel better now that he'd be able to actually use his 75% yield increase on all those yields that used to be just 1 in Ancient. Right now, finding Mercantile, Culture, and Militaristic CSs in Ancient is like "Meh" while finding a Religious CS is totally game warping for him. With these changes I think it would feel a lot more balanced across the board (I might still be sort of "Meh" about finding Mercantile CSs but it's at least a little better).
I think a free 30 faith from finding a religious CS early isn't so terrible. Siam still has to build a shrine to get the rest of the way to a pantheon, and religious CSs tend to be the least common type I think? If you're able to get some barbarian kills or some other means of gaining extra influence (donating a warrior) then more power to you- at least you did something to earn it. You probably had to send your initial warrior and pathfinder over to ensure the kill which means you left your capital open to barbarian attack so it's not without cost or risk.