Most right-wing movements of which I am aware would definitely like to be seen as apolitical (and thus reduce the critical eye aimed at them). But the line you can draw from there (and similarly from "apolitical" rage-movements like GamerGate) to the current state of things is a straight one.
This seems at odds with Stephen Colbert's famous quote "Reality has a well known liberal bias". Regardless, there isn't anything in MGTOW that indicates either left or right wing views as far as I can tell