My brother made a very good living working on court cases near Baltimore (ship yards), litigating (for the ship builders) private settlements with the workers dying from asbestosis.
He worked on a few old vehicles and he did not even want to chance inhaling asbestos brake linings.
Better safe than sorry - it is so simple to wear a mask and clean your work clothes.
Mike addresses, in the first reply, prudent precautions that are quite easy to do.