I'm not familiar with Greenway's work. When the 1998 thread on pagan music (not the recent one) drifted into a discussion of Joseph Campbell, I noted that I thought Campbell had a Jew-hating streak in his personality, but that the question of whether he had such a characteristic was separate from the question of whether it influenced his scholarly work. Maybe you'd find the same distinction to be useful in your evaluation of Greenway.

Even if Greenway's political views influenced his scholarship--say, by influencing his choice of questions to research--that doesn't mean that his work is totally useless. If nothing else, it might provide useful data for how scholars' political opinions influence their scholarship!

T.