Asbestos shingles are safe as long as they are not damaged, crumbling or otherwise in general disrepair. Asbestos is relatively safe until when disturbed or broken the fibers become airborne and then the trouble begins.
It cannot be removed by a general contractor that is not licensed to handle asbestos, same goes with anyone who handles this product. Make sure any company you have doing the work is licensed to handle asbestos....VERY IMPORTANT.
There are companies around that will repair damaged asbestos shingles and then coat them (encapsulate) in a bonding agent, that is both safe and cosmetically appealing.
This page should help you:
Asbestos Shingles on Your House? What to Do When They Need to be Replaced!