Unless you're fish poo or bird poo, I wouldn't worry too much. The animal digestive tract is an active transport system operating at the molecular level and reasonably selective about hydrocarbons.

The problem is that essentially any modern polymer product isn't pure hydrocarbons. Consumer plastics rely heavily on plasticizers, which change the physical characteristics of the material. The effect of plasticizers on health isn't really widely understood.

I agree with the OP's point that the headline is alarmist. Though I find the idea of even few dozen coke bottles per km^2 at the ends of the earth pretty depressing.

Between the low concentration, UV exposure, oxidation, acidity, and salinity, I suspect most the stuff is long gone. You almost certainly get more exposure eating off plastic plates, using plastic silverware, drinking from red party cups, etc.