There are too many nonprofit or public policy institutions to list, of course. Exception: I do have most of the state-level public policy institutions listed below. Note the political agenda.
My suggestion is that you note any specific names you already know, as well as those you encounter as you are learning about your topic, then google to scope out their websites for their take.
In my previous example, I knew about SCRAPS, Spokanimal, and Spokane Humane Society from having adopted pets. I then ran across ASPCA, the Humane Society, and American Veterinary Medical Association while looking for statistics. The more you peruse, the more names you'll run across...