At the moment there are several cultures in the game with a stability bonus - Zhou, Swahili, Poles, Austro-Hungarians, Italians and others. But they are weaker than other cultures, since high stability (100-91) only gives +1 influence on the population (correct me if I'm wrong or missed something). For the same reason (and also because of the terrible block cost scaling) there is no point in building community blocks - it's cheaper to build infrastructure or buy more luxury resources.

To change the current situation, I propose to introduce additional bonuses from high stability (perhaps provided by the new Civic) - something like + 25% to FIMS.

Your opinion?

+25% to FIMS might be a tad too powerful, but I do agree that high stability prior to the contemporary era needs some sort of a buff. Stability as a mechanic is a wee bit broken at the moment as most players may experience ups and downs from eras 1-5, making any enhanced bonuses worth it, but once you're well into the contemporary era it's pretty easy to maintain, making any high stability buff practically permanent. The intention behind high stability civs is to compliment expansionist civs and ones that prioritize mass district construction, but as a standalone, they can feel a bit weaker than ones with direct bonuses. That being said, The Swahili and Poles are pretty strong choices in their respective eras, and the Zhou +2 per district can really shore up later civilizations that are in the process of mass constructing districts. 

This is totally out of scope but food for thought: https://www.games2gether.com/amplitude-studios/humankind/forums/169-game-design-and-ideas/threads/47149-how-about-a-sliding-scale-for-stability?page=1

If you don't have access to luxuries it can be quite difficult to keep high stability.

This happened to me when I played a game with luxuries set to low.

Is double the influence from population enough of a bonus? Not sure.

But if you don't go into Freedom ideology it will be the main source of Influence for the empire.

Also, a few wonder bonuses need the city to be in high stability, but that's a minor point.