Setting aside the fact that the purported harms (if specified at all!) are nearly always based on confounded observational studies and/or animal models at doses that may not bear any relationship to the doses you're being exposed to in real life, the claims for any particular item are usually presented out of context. For example, is exposure at X<10 parts per billion compound Y meaningful, as a human who lives in the real world? Typically, nobody knows, but you can nearly always find an "expert" who will confidently claim that any exposure is "dangerous."
Skepticism and awareness of risk magnitude is essential when reading stuff like this. Academics who specialize in obscure areas love to get their name in the press, and the easiest way to do that is to go to a reporter and make vague and irresponsible claims about risks to human health, even if those risks are very, very small. [1]
For what it's worth, I have a Teflon pan, I've used black plastic spatulas in the past, and I'm not worried about it. Compared to the reasons I already know that I'm likely to die, these things are irrelevant.
[1] Case in point: I knew a tenured professor at a prestigious university who was absolutely convinced that if we all continued to eat beef, we'd be looking at an epidemic of vCJK (aka Mad Cow Disease). Saw a lecture from this person on the subject over a decade ago now, where the risks were presented as looming and absolute. We're still eating beef. Guess what hasn't happened since then?