According to a story published yesterday on Modern Farmer's website, a byproduct of Greek yogurt, acid whey, does indeed pose environmental problems. According to the article, "... [W]hey decomposition is toxic to the natural environment, robbing oxygen from streams and rivers. That could turn a waterway into what one expert calls a 'dead sea,' destroying aquatic life over potentially large areas. Spills of cheese whey, a cousin of Greek yogurt whey, have killed tens of thousands of fish around the country in recent years."
For now, it seems that the big producers, like Chobani, are working to dispose of the whey in an environmentally friendly manner. The story chronicles this process, as well as the many ideas circulating about how all this acid whey could potentially be put to use (baby formula? electricity production?). After the story was published on Modern Farmer, Chobani issued a statement on its own website explaining how it disposes of its whey.
But the main point is that there currently is too much whey, not enough uses for it, and the amount of whey is only growing along with the demand for Greek yogurt. If the stash of passionfruit Chobani in my fridge is any indication, that demand isn't going anywhere.