A comparison with punk rock actually illustrates very clearly why Black Metal is incompatible with left-wing content. Punk rock was a social movement from the very beginning, and because criticism of capitalism is not exclusively left-wing, it was only a matter of time before punk came into contact with explicitly right-wing ideas, eventually giving rise to RAC as a legitimate genre.
Black Metal, however, was spiritually rather than socially oriented from the outset. And in this view, spirituality is fundamentally incompatible with a left-wing worldview. The left tends to regard mythic thinking as alien and sees traditions, customs, and rituals as relics of the past that ought to be overcome. In that sense, such thinking stands in opposition to the spirit of Black Metal.
Unlike RAC, where a right-wing worldview merged organically with punk rock, a left-wing worldview can only be inserted into Black Metal as a foreign body. A foreign body that Black Metal instinctively rejects. That is also why so many bands attempting to play supposedly left-wing Black Metal end up sounding mediocre or outright poor. The synergy between spirituality and art is missing, because everything feels forced and unnaturally combined.
Left-wing Black Metal remains an oxymoron, and so far no band has truly managed to resolve those contradictions.