I haven't read Bloom. But I am such a Heidegger partisan that I knowingly put myself in "harm's way" as his apologist. To me, the boldest indictment of relativism is Kierkegaard's exploration of leveling in his The Present Age. In no way does Heidegger refute that work; quite the contrary.
It is said that MH's only comment on the Holocaust was something like: Sure that was bad. But so is mechanized agriculture.
That certainly is a stupid moral equivalence, if it is meant to be an equivalence. Moreover, George Orwell came to a more humane conclusion about mechanized farming when he figures out how an outmoded plow (found in an abandoned Spanish barn) is intended to be operated. Hmm, I seem to have strayed off-topic.
Anyway, Heidegger staunchly condemned the dehumanizing tendencies of modernism alluded to in the Lev Navrozov article of this thread.
And loved Nazism.