If the building is city-owned and demolition has not begun, contact the mayor by email and CC their executive assistant (they will nearly always be the one to respond). Be very clear about your intentions and why you wish to enter the building. It usually helps if you include a “historic preservation” aspect in the summary of your goals. Here’s an excerpt from the last email like this I sent 3 weeks ago.
I then go on to explain that the facility in question could be considered historically significant, and that I would appreciate the opportunity to help preserve some of the equipment and signage. Many times the kicker for me is that, if truly a significant building, I offer to donate signage back to the city or to their historical society. It certainly helps in your case that the 1920s and 1950s school buildings could fit the description of historically significant.
If the building is privately owned or preparations for demolition have begun, contact the demolition contractor directly. They will usually have a sign out front advertising the structure as one of their job sites. Or, you can check the City/Village Council website (if applicable) to see which firm the bid was awarded to, or in the case of a privately owned building, who pulled the demolition permit.
I’ve used both methods and have had success. As a side note, if you aren’t 18 yet, you may be at a disadvantage as many times you will be asked to sign a liability waiver as well as an NDA.
I’m going to put in here as a disclaimer that my salvage activities have always been lawful. In addition, this should go without saying, but please do not harass city officials or demolition workers for these parts based on my advice. Asking once is enough. If they say ‘yes’, great! Otherwise, just move on.
If you are concerned with asbestos, a P100/HEPA respirator offers adequate protection. If you suspect the facility has large amounts of friable asbestos fibers (ex. pipe insulation, damaged ceiling tiles) these filters are in your best interest if you will be entering the building. Encapsulated asbestos (wallboard, cement, corrugated siding) are not immediately dangerous unless disturbed.
A respirator is likely not necessary if you expect this to be a one-shot deal. If that’s the case, a disposable dust mask will suffice. Your exposure will be low, however there is never a “safe” level of exposure. It’s up to you to weigh the risks.