IIRC, a city's Stability doesn't immediately update to its new Stability level whenever its Stability changes. It normally changes by increments of 5 stability per turn, until it can reach the new Stability level (if the difference is less than 5, it just updates by the difference iirc).

With Censored Arts, I think those increments instead become +4/-4 instead, and I guess Free Arts would change that to +7.5/-7.5? I haven't actually checked to see if that is the actual change, but that would be my guess.

tl;dr: I think Censored Arts makes stability changes slower, and Free Arts makes stability changes faster.