I've been in several stratas including multiple councils, and seen several taken to the courts part bullshit bylaws and lose. One strata actually tried to restrict people's ability to have a non-married partner overnight. That... did not go over well as it became obvious that the real target was senior members intent on driving out younger residents, as well as a bit of power-tripping.

By that same notion, yeah they can absolutely fine somebody for damage to common property etc during installation, and I've seen that happen (i.e. one resident knocked bricks out of they chimney to side-vent a gas-fireplace install) but an outright ban on AC installs when we're seeing growing heatwaves could likely see a successful challenge for personal health and safety reasons among others. Just depends on whether the resident has the time and resources to fight it.