Should I take it that Peterson and Harris are both moral realists and interpret their words in that light?
Yes. I believe neither Peterson nor Harris is a moral anti-realist.
So, if they’re moral realists, then “not throwing away the concept of good” means not throwing away moral realism; I think I understand what that means in this context.
Yes. I believe neither Peterson nor Harris is a moral anti-realist.
Yes. I think you understand the debate correctly.
Harris is both a moral realist and a naturalist. He thinks moral truths can be derived by science. https://en.wikipedia.org/wiki/The_Moral_Landscape