You have a vastly higher risk of contracting skin cancer from old engine oil than you ever have contracting measothelioma from asbestos brakes.
Do you fill your car up with unleaded petrol? It contains Benzene, an agressive carcinogen that you breath in in large quantities while filling up.
The issue with brake fitters was down to using airlines to blow dust out of the brakes constantly, day in, day out that put large quantities of asbestos dust into the working environment they were breathing in every hour of their working day.
Very simple precautions remove any risk to infinitesimal.
Wash out the brakes with brake cleaner rather than brush or blow out the dust, use a dust mask.
They have still to find a superior material than asbestos for brake linings. Some of the synthetics have a higher friction rating, but they are scary expensive, they wear at a frightening rate and destroy disks with equal rapidity.