Is it correct to say that “some degree of pollution is an inescapable consequence of the Second Law of Thermodynamics”?
Yes, this is true. However, the question is where that increase in entropy occurs.

Since the industrial revolution, life on earth is a bit one-sided, with humans controlling the chemistry going on, and a lot of it. When we burn fossil fuels, there is an increase in entropy on earth. Before that, one organism's waste was some other organisms food, and the entropy increase occurred mostly in the sun (giant nuclear reaction slowly going towards equilibrium).

Humans (and all other animals) benefit from the $\ce{O2}$ "pollution" from cyanobacteria and plants. Plants benefit - to a degree - from the $\ce{CO2}$ "pollution" from animals. However, when global concentrations change too fast, some species might benefit a lot, but many other species will go extinct.

If the "plastic ocean" had built up over millions of years instead of 50, some microorganism that uses the polymers as its primary source of food might have evolved, and there would be a cycle instead of a build-up.