From what I could tell in the video, bisphenol a's a petroleum derivative that is used to harden polycarbonates. The other one, pthalates (also a petroleum derivative) is used to soften PVC. So technically, not made out of plastic, but used to make plastic.

Edit: Realized I misread your comment. Yes, the problem is with some plastic products, which use these chemicals (but not all, since the video mentioned that one hospital using safe plastic products).

I have the impression it's some plastics but not all. A rule of thumb many people up here use is to avoid plastics with recycling number 6 (polystyrene) or 7 (polycarbonate). These are said to be the worst.

Alex, does the film contain specific recommendations to consumers? (Normally I hate using the word "consumer" to mean "citizen" but in this case it could hardly be more accurate.)

Somewhat--but phthalates are also in cosmetics, carpeting, deodorants, and many other household items.