> Perhaps those items are made from a material that the manufacturers know has potential health implications and that's why they're carefully not saying what it is?

Unlikely. It's more likely that they don't know, because they didn't look too hard.

The reason it's not recyclable has nothing to do with that, though. It's not recyclable because plastic recycling is very difficult, many plastics can't be recycled, and of those that can, any contaminants will ruin an entire batch. Food is an example of such a contaminant.