Is there any specific evidence that they are a risk to human health?

I mean, I get the instinct that foreign-entity can't exactly be good for me, but the same instinct applied to GMOs, and as far as I know organic foods have never yielded any sort of statistically visible health impacts.

Plastics earn their keep in general by being non-reactive and 'durable', so it's not entirely shocking if they can pass through (or hang around inside) the body without engaging in a lot of biochemical activity.