For example, consider this comparison: when you take a pill of some drug, say an aspirin tablet, how much of the active ingredient (aspirin in this case) are in that pill? And how many bottles of water would you have to drink to put the same amount of nanoplastics (treating them as an "active ingredient") into your body?
Here's a back of the envelope calculation: suppose the concentration of nanoplastics is 10 nanograms per liter (about what is claimed in the article). A liter is about one (fairly large) bottle of water, so say 10 nanograms per bottle. A standard aspirin tablet has 325,000,000 nanograms (325 milligrams) of aspirin in it, or 32.5 million times as much active ingredient. So you would have to drink 32.5 million 1-liter bottles of water to expect the same general order of magnitude of "active ingredient" effects on your body as one aspirin tablet. If you drank one bottle of water per second, it would take you more than 10 years to drink that much water.
So I don't see any reason to forgo bottled water on these grounds. Certainly not in favor of tap water, which is much more subject to how careful your municipality's water purification process is (not to mention various possible sources of contamination in the water lines between the purification plant and the water tower and you).