Probably. But do you really think homosexuals don’t internalize homophobia or women don’t internalize misogyny in our current society? Or that racial minorities don’t internalize all of the stereotypes associated with their identities? If people weren’t deeply sensitive to those pervasive messages and prone to be structured by them on an unconscious level, we wouldn’t have women with devastatingly low body images, or relatively high rates of depression and suicidal impulses among homosexual adolescents, or measurably different economic futures for children of different races. Is it lamentable? Absolutely. Is it inevitably and universally the case that people are determined by their social, racial, and gender position? Of course not. But is it common? Hell yes.
Arendt didn’t identify with feminism either. We can reproach her for that, as well - and plenty of people have - but I’m not sure it would be useful. We live in a culture that by and large tells us that our differences are inescapable and to be embraced, but that attitude is historically contingent. From another, not so distant perspective, the idea of universality offered the possibility of liberation. Only by denying or subsuming our differences could we reach the subject or citizen who was absolutely equal to all others. Arendt was born in that era - after all, her family was by and large very highly assimilated. So we could reproach her for wanting to escape her particularities, her Judaism, her gender, and simultaneously, for not escaping them enough (hence the tortured relationship to Judaism), but doing so would be deeply ungenerous and shallow.
As for why we should read Heidegger: how about because every single major thinker in the 20th century who came after him read Heidegger and took him seriously? Even the Jewish ones. If Levinas, Sartre, Blanchot, Derrida, Merleau-Ponty, Marion, Ricoeur, and co all thought he was worth grappling with, even if they disowned all relationships with him personally and denounced him for his Nazism, shouldn’t that make us hesitate to discard him?
Or how about this reason: Heidegger came on to a philosophical scene that by and large exalted the human subject as the only creature that is capable of total self-awareness, that can now and master the world (think Hegel, Schopenhauer, etc), and suggested instead that, no, the human always finds himself thrown into a situation that he can never entirely escape and that makes certain possibilities live and certain dead. We are hemmed in by our finitude and do everything in our power to escape it. We lose ourselves in curiosity (think the Internet here) or idle talk, we subordinate our own voice and actions to what “one” does, and the only time we’re really capable of gathering our life into any sort of whole or perspective is when we face the inevitably of our own death, the possibility of our impossibility. At that moment we can flee - and likely will - or we can engage in the world with a whole-hearted notion of care (Sorge). But that recognition of the possibility of impossibility, that momentary, visceral revelation of the strangeness that there should be something rather than nothing, is a source of terror, of resolution, and a source of wonder. It’s the source of the wonder that makes all thought possible. If you want to find proto-fascism in this, go ahead, cite some passages. But my sense is that Heidegger’s Nazism was unworthy of his thought at its best.
Finally, “the banality of evil” is not supposed to explain anything about evil. It’s not supposed sound “meaningful.” It’s entirely designed to combat the effort to understand evil and give it meaning. It’s designed to alert us to the danger of evil that can, “overgrow and lay waste the whole world, precisely because it spreads like a fungus on the surface.” Arendt thought, to some degree, that this tendency could be combatted by teaching people how to think. Radical evil, a la Rosenbaum, leads to a radical passivity, precisely because it’s a way to avoid thinking. It gives a sort of easy meaning that allows us to label evil in degrees, say evil people always know they’re evil, and to file everything away in a meaningful universe divided into good and the axis of evil. To wit, from Arendt’s collection of Jewish Writings:
“The idea that evil is demonic, which, moreover, sees its precedence in the tale of the fallen angel Lucifer, is extraordinarily appealing to people…Precisely because these criminals were not driven by the evil and murderous moments that we’re familiar with – they murdered not to murder, but simply as part of their career – it seemed only too obvious to us all that we needed to demonize the catastrophe in order to find some historical meaning in it. And I admit, it is easier to bear the thought that the victim is the victim of the devil in human disguise – or as the prosecutor in the Eichmann trial put it, of a historical principle stretching from Pharaoh to Haman – the victim of a metaphysical principle, rather than the victim of some average man on the street who is not even crazy or particularly evil. What all of us cannot cope with about the recent past is not the number of victims, but the shabbiness of these mass murderers lacking any sense of guilt and the mindless shoddiness of their so-called ideals.”
There's a discussion to be had about these issues, but this isn't a discussion. It's a tone deaf, dismissive, poorly researched and poorly thought out screed against two caricatures who bear almost no resemblance to the thinkers in question.