Hi barkingtrout,
I would avoid PVC (which isn’t breathable anyway) because of potential toxicity issues and leaching but I wouldn’t consider any of the breathable/waterproof membrane protectors (which are mostly polyurethane membranes) listed here to be toxic. If you are at all concerned about any toxic VOC’s or chemicals then two of them (Naturepedic and Gotcha Covered) are organic and one of them (Protect-A-Bed) is Oeko-Tex certified both of which would provide you with some independent assurance that they have been tested and certified for harmful substances and VOC’s. Of these the Protect-A-Bed protectors are the most economical.
It’s always easier IMO to take a “bottom line” approach that involves independent testing for harmful materials and VOC’s than to try to learn about and analyze the actual chemistry of the hundreds of different variations of each type of plastic when the specific information about how each of them is manufactured and the exact chemicals each of them use is not available.
Phoenix