I think the definition of moderate is someone who is not at either extreme, but sits more closely to the center of things. They can still be left-leaning or right-leaning.
However you want to define it, the problem at the moment is that the extreme left have made everything an "us or them" scenario. Either you are extreme left or you are far right/nazi and there's nothing in between for them. They even eat their fellow leftists alive, if they are too moderate in their views. Purity tests apply.