Per the US Agency for Toxic Substances and Disease Registry, “Developing fetuses and infants are not likely to be exposed to asbestos through the placenta or breast milk of the mother. Results of animal studies do not indicate that exposure to asbestos is likely to result in birth defects.”
For something to pass into breastmilk it must first enter the mother’s blood, and asbestos only enters the blood in extremely low amounts (if at all). Per the US Environmental Protection Agency, animal studies in which animals were fed high doses of asbestos have not shown adverse toxic effects.
Asbestos exposure primarily results from inhalation of air containing asbestos fibers, which can result in lung disease or cancer. Asbestos does not dissolve in the air or water, but is present as suspended particles (dust, etc). The asbestos acts locally – exposure occurs when asbestos fibers come into contact with the lungs or GI tract. It usually takes long-term exposure (15-40 years) for health effects to appear.
If asbestos is not disturbed or damaged (so that particulates can get into the air), then it is not hazardous. Removing asbestos (also called asbestos abatement) can be hazardous because of the particulates that get into the air during the removal.
Some of the things that are done to reduce the inhalation risk during removal include blocking off the removal area from other areas with plastic sheets and duct tape, wetting down the asbestos (this is very important and minimizes the particulates in the air), using special HEPA vacuum cleaners, etc. Asbestos abatement workers wear coveralls, boots, gloves and respirators. All of the wet asbestos materials are double sealed in labeled plastic bags for disposal. This information for homeowners has a general overview of how an asbestos abatement is done and should give you a general idea of whether the workers are following proper procedures: Asbestos Removal, Handling, and Disposal Guidance for Homeowners .
If the asbestos removal is done properly, then you should not come into contact with asbestos fibers. If you have doubts about whether the removal is being done properly, contact (in the US) OSHA or the EPA.
Asbestos from the US EPA Integrated Risk Information System
Asbestos Removal, Handling, and Disposal Guidance for Homeowners from the Utah Department of Environmental Quality, Division of Air Quality
Agency for Toxic Substances and Disease Registry (ATSDR). Toxicological Profile for Asbestos. U.S. Department of Health and Human Services, Public Health Service. September 2001.