Actually yes if you'd call someone a misogynistic slur, even while experiencing trauma, you would be misogynistic. Because that comes from your subconcious. Severus was a victim and the reason he joined the death eaters was due to his social and economic victimization, however he was not a complete mindless idiot who didn't understand anything. He was clearly anti muggle (and although yes his prejudice was influenced by his horrible father and home he still encountered normal muggles so he didn't only have negative experiences with muggles, he could clearly see that some of them are not violent. He was an intelligent man I believe his brain could work this out.) And even when he's a big victim it doesn't mean he is entirely blameless of his words and actions and what they say about his morals. Him calling Lily a mudblood is a clear indication that he doesn't view muggleborns the same way he does other wizards and has clear prejudice. He did not only use that word once but many times - according to Lily. I'm not denying your other claims, you just seem to talk about Severus as if he wasn't an asshole who held bad views, because he was victimized. Do you think he was a good person in a bad situation? Not at all. It is fine to criticize his actions and morals while still taking into consideration that he was a victim and a lot of his decisions were a result of that.
I don't see it that way, but this is a matter of perspective. I might have internalized misogyny or internalized racism, but literally everyone has this, absolutely everyone. It's not the same as, at some point, saying a misogynistic slur to a friend in a moment when I'm about to lose my mind, versus constantly doing it. There's a difference between having a generalized attitude and letting something slip at a specific moment. And if we’re going to start categorizing people or characters based on something they say at a particular moment, then I’m sorry, but we should accuse everyone because there’s no one, absolutely no one in this society, who, even if they are very conscious and deconstructed, hasn’t made problematic comments or used harmful adjectives at some point.
I don’t deny that Severus had prejudices against Muggles, but his prejudices stem from a completely different basis than the prejudices Lucius, for example, might have had. Severus’ prejudices come from his own negative experiences with Muggles, from the fact that the Muggles he’s known were literally awful. Is it wrong for him to have prejudices against an entire population because of that? Yes, but it’s also understandable that he has them. I mean, I spend my life insulting cis-hetero men because they’re the types I have sex-affective relationships with, and I’ve had countless bad experiences with them. Could I be labeled as misandrist? Probably. Am I a bad person? I don’t think so. The problem with these issues is that people tend to see things in black and white, but real life is very diverse. You shouldn’t focus on the tree but on the forest. But well, that’s just my personal opinion.
Deep down, I’m very critical of Snape, even though it might not seem like it. What I don’t like is when people make arguments without considering the context and criminalize him without exploring the reasons for his actions. Was it wrong for him to call Lily a Mudblood? Yes, but we must take into account the context of when he did it, and the fact that it was an isolated incident, not a constant. It’s likely that what he wanted was to hurt her, just like when I call my friend a slut, and sometimes you say things to people because you know it will hurt them, not because you genuinely think that way. Anyway, I would be more critical if it were someone else, but in Lily’s case, it’s hard for me to be completely impartial because she ended up marrying an unpleasant, bullying, abusive person, and honestly, I think Severus fell short. If I had seen my supposed best friend half-smiling at my bully, I would have punched her in the face. I swear, I would have destroyed her and then publicly humiliated her, making her wish she had never been born. But as I’ve said before, I’m a very resentfully aggressive person xD.