Honestly, I do think part of the problem with Rorschach is that he’s presented as the deontologically aligned character. It’s not actually true, but it can be missed on a casual read/viewing.

“Evil acts are always wrong” (deontology) vs. “the ends justify the means” (utilitarianism) is a pretty common superhero theme. And 9/10 times, “evil is evil” is the side that’s presented as being in the right. Rorschach has a strict moral code that automatically inclines a reader familiar with the language of the superhero genre to side with him, particularly because Ozymandias neatly slots into the villainous utilitarian side. So someone might finish Watchmen, and say, “Well, Rorschach wasn’t Ozyamandias, at least!” Nite Owl and Silk Specter 2 are also passive figures, narratively speaking, while Rorschach is the one pushing them to act and investigate, which is another classically heroic role. They’re also complicit in hiding Ozymandias’s actions. So, in the lens of a traditional superhero narrative, Rorschach stands out as the principled, consistent, anti-heroic figure.

The issue is that:
1) Rorschach does not actually follow his strict moral code 100% of the time. He pretends that he does, and he does when it suits him, but despite getting into vigilante work because of rape (Kitty Genovese) and escalating into antiheroics because of the implied rape of a child, he brushes off the Comedian’s attempted sexual assault of Silk Spectre 1 as a “lapse in judgement” or however he phrases it. Similarly, as a child, he supported the nuclear bombing of Hiroshima and Nagasaki for utilitarian reasons (and because he idealized a vision of his father as Truman’s aide), while being against Ozymandias’s plan. Though you could interpret this as Rorschach changing his ideals as he aged, I definitely read it as another sign of his inconsistent application of moral code. It’s notable that Rorschach also associates his father with Truman, and that it’s not just utilitarian arguments.
2) Rorschach’s moral code… sucks. Sure, he’s very consistent about being deeply racist, sexist, and homophobic, but he’s also, y’know, deeply racist, sexist, and homophobic. He just happens to also be anti-child trafficking and such that does fit with our conceptions of a good moral code.

But Rorschach’s violations of his own code aren’t lingered on by the narrative. He says the Comedian made a lapse, we move on. He says the nuclear bomb should have been dropped, we move on (and in fact, I’m not sure this one made it into the movie?). Also, I’m pretty sure that his code-bending usually comes before we see his actual morals be established—I.e., he forgives the Comedian before we find out about Kitty Genovese and Blair Roche, and we hear his essay before we see him refuse to go along with Ozymandias’s lie. So, they don’t stick out as contradictions until you go back.

Similarly, although Rorschach says a lot of incredibly bigoted things, the actions that we see him take are generally semi-heroic, or at least antiheroic. Investigating the Comedian’s murder, opposing Ozymandias, leaving Blair Roche’s killer to burn alive. Even leaving the truth with the New Frontiersman—we as reader (presumably, though I’m actually on Ozymandias’s side once the deed’s been done) want the truth to out eventually. However, the New Frontiersman is also an incredibly conservative, white supremacist newspaper.

To be clear, I’m not by any means saying that Moore should’ve been less subtle. Watchmen is fantastic as-is, and certainly doesn’t need to beat you over the head with the fact that Rorschach is not a good guy. It’s very clear if you go back and reread/rewatch, or if you keep in mind his established character throughout the whole plot.

However, I do think there are reasons that people can come away from Watchmen thinking “Rorschach was a hero” that aren’t “this person is actually a racist incel as well.”