I suspect that far more folks are hurt by entering a burning building to fight a fire, than will ever suffer from asbestos exposure.

In other words, one has to keep his risks in perspective.

In the broadest sense, asbestos was used in so many products - nearly everything - that I'd suspect any car or building made before 1974 has some form of it somewhere. Yet, that paints a distorted picture.

If the asbestos is part of a matrix, such as in cement roof tiles, or vinyl floor covering, or auto brake pads, it is almost impossible for them to ever present a hazard by mere "exposure."
Even exposed, if the fibers are of a longer type -such as was used in firefighter coats and 'hot pads,' the risks posed by it is slight.

A different picture is painted when the fibers are short, and are being sprayed on pipes. It's no accident that the major studies of asbestos risk have involved folks who sprayed the stuff on shipboard piping!

Then, there is the matter of identification; I was recently at one job, where the beams and rafters in the "atic: were coated with a dusty, flakey, white fireproofing compound. Testing proved it to be a cement product- no asbestos at all.
The plaster that was used for the ceiling - plaster applied to wire lath - DID test positive, however. Go figure!

As a firefighter, well, you really have neither the time, nor the equipment, to make the proper tests.
You're suited up like spacemen, breathing pure canned air, and perfectly deployed to hose off afterward... where's the risk?
If there's a risk to anyone, it's to the guys who have to clean up the mess later.