Teflon, PLA, ABS, resins, foams, etc... are all plastics, but they are so unrelated outside their long chains, its terrible to stereotype them all into one category.
You aren't going to get cancer from PLA or Teflon, but rather the manufacturing process. You can eat these plastics as far as I know and you'd be fine.
Eat something with BPA in it, you are probably going to have a bad time.
Maybe the solution is better labeling. I know its near impossible to have perfect consistency in plastic manufacturing(I worked in foam, mind boggling we consider testing these foams one time, and considered it the same foam for the next 8 years). However, knowing precursors, additives, and potentially process would make a huge difference in our ability to track problems.
EDIT: Someone called out PLA as potentially dangerous. After looking it up, I'm skeptical of the oxygen double bond attached to a carbon attached to an oxygen. The wikipedia article had no health concerns, but that carbon atom seems ripe for reaction. Let me change my answer on PLA to 'I don't know'.