What happened before the recycling movement was that Western waste was burned in Western waste disposal facilities. This created a ton of toxic shit. Shipping it off to Asia or Africa kept our skies clear. So the recycle lie was created.
If it's below 400° (as happens if you burn plastic in your backyard or fireplace) you'll release dioxins, which are persistent fat-accumulating toxins, and fluorine and bromide compounds which are typically bad news to anyone downwind.
It does depend on the plastic you burn though. Some are worse than others, but 1000°+ controlled incineration is typically fine for all.
I was admiring their efforts until I noticed a smouldering rubbish heap in their back garden. Sure enough, they burned all their plastic and other waste.