Plastic is not very reactive. This property makes it generally not directly harmful to organic health, but also notoriously slow to decompose, causing huge amounts of pollution. I think it's misleading to compare it to asbestos.
To be clear, asbestos is less reactive than plastic (particularly most thermoplastics) by a wide margin. One burns, the other will not. Asbestos is closer to glass. It requires incredibly high temperatures to turn it into glass as a matter of fact, as that's about the only way to dispose of it permanently.