Jimmy’s point on the building being possibly designed in a way or limited by some variable so as to discourage or negate the installation and use of a/c units may well be valid. At this stage we don’t know.
I suggest that 3dpotato ask the s/committee or manager “how did the by law come about” and “what’s its purpose”?
Don’t be too specific in the questions. And email them, don’t ask in person.
If the committee’s answers do not rely on design or electrical capacity available in the building, then I’m with Kaindub: the by law is harsh and oppressive and worth a challenge.