No insulating materials on the market in Canada today have asbestos fibers in them. Most of the scare a few years back about asbestos came from acoustic tiles, asbestos linings in ventilation ducts, and asbestos insulators in heating devices such as hair dryers. It was also discovered that Vermiculite insulation sold by the Zonolite company was contaminated with asbestos. Many homes do have this insulation in their attics. Check with your local health department for the latest recommendations for dealing with this problem.
Fiberglass and mineral wool products do have small fibers that can be irritating and long-sleeve shirts and cotton face masks should be worn while working with these products.
Some companies that would like to make you afraid of fiberglass (in order to buy their products) point out that fiberglass fibers are about the same size as asbestos fibers. True, but the difference is that although an irritant, the human body will simply dissolve the fiberglass fibers while the asbestos fibers remained in your lungs as a foreign substance for the rest of your life.