I don't know if those terms state that the dogs are unnatural, so much.
I think the words "mix breed" or "mutt" just tell what type of dogs they are.
At least thats what I think.
You do raise some interesting points though.
I am a owner of a rescued mix breed dog and proud of it.
so to me I don't find those words to offesive,
unless you use them on people. lol