Any work that employs satire, irony, or sarcasm in a proper and correct fashion requires that some portion of the audience be confused, or even hurt, by the work. Because ambiguity is not a bug, but the central feature of any work that plays with or invokes satire and irony. Simply put, the possibility that the audience can misunderstand the message is necessary to the proper conveyance of the message. This ambiguity is not a bug - it is the distinguishing feature.
I would turn this around slightly: when writing a parody, you ought to keep Poe's Law in mind. It may be ambiguous at first, but by the end, you should make darn sure people know you aren't
actually advocating for eating babies. You're probably right that achieving understanding by 100% of the audience is asking too much (You probably won't get that even if you include an explicit disclaimer.), but if the nazis think you're laughing with them and not at them, then your parody isn't very effective.
when people say that Gygax had some sexist attitudes, I recognize that this is a statement that isn't about me, and doesn't attack me as a person. I can still appreciate the things that I loved about those early D&D books while still understanding that they had issues.
If most people understood that criticizing a thing or a person who made a thing is not a personal attack on everyone who likes the thing, the Internet would have so many fewer arguments as to be completely unrecognizable.
Does it follow that including a sexist character or culture as part of a game means that the game itself is sexist?
If done with care, not necessarily. Let's take as an example the sitcom
All in the Family. The main character, Archie Bunker, is racist, sexist, antisemitic, and homophobic, and he's not shy about it. But the main point of the show is that he's wrong about those things: not an irredeemable monster, but clearly in the wrong nonetheless.
Some folks may hear enough of that nonsense in their own life that they don't enjoy watching such a character, no matter how often he gets his comeuppance, but it's hard to argue the show itself is racist, sexist, antisemitic, or homophobic.