OMG I saw your tags on that one post, and I would die to hear your Homura thoughts! I love all the Homura art you reblog! What things do the fandom do that mischaracterize her so much that you can tell in 3 words that they see her differently?
Oh dear oh dear, I've opened my thoughts up for examination.
I have a lot of thoughts about Homura, and I'm a lot better at expressing those through fiction than I am just talking about her. I'm also hesitant to actually point out what sort of attitudes I hold in contempt because I'm a fan blog, but there's definitely some things I can share. Keep in mind that nothing I say here is intended to be a sincere criticism, but simply a matter of how I, personally, interface with fan media surrounding PMMM (and Homura in specific):
There's a whole genre of post that basically starts with "OMG PMMM is sooo crazy like imagine that..." and then roughly recounts the plot from Homura's perspective: of being trapped in a never-ending labyrinth of suffering to save your crush, only for her to turn into a metaphysical principle / god. The reasons I just instantly scroll past things like that are twofold:
One, I think simultaneously adopting a hyper-literal "imagine all of these events as things that happened to you" perspective and a "this is so buckwild and weird" perspective at the same time distorts what it's trying to represent - that is, Homura's perspective. Rather than directing the reader to actually imagine Homura's perspective, it says "imagine Homura's story as it would look to me, the viewer." If you want to imagine things from a character's perspective, you need to also imagine how they think and feel, and how that's different from you, the viewer.
Two, these sorts of posts almost always frame Madoka as Homura's crush, or her girlfriend, and not the thing that actually makes Homura's wish meaningful: Madoka is the person who saved her life. Not only did Madoka literally slay the witch that would have caused Homura to kill herself, Madoka also instilled her with a will and purpose to continue living. Up until near the end of Rebellion, I think that Homura's romantic feelings for Madoka are always secondary to the fact that Madoka saved Homura from her own emptiness.
2. Basically anything that's got a comedic tone with a punchline about how Homura's feelings towards Madoka are unrequited. This stuff bothers me less, because I mostly see it as an easy misinterpretation of the text that is downright valid if you haven't watched or don't like to think about Rebellion. I just don't like it because it makes for a less interesting dynamic (and a less-interesting Madoka, IMO).
3. I think this is a pretty common attitude among Homura enjoyers, but anything that tries to paint Homura as either totally selfless or totally selfish makes my eyes glaze over.
4. Homura "would sacrifice the world for Madoka" or similar type stuff about how Homura is completely ruthless in pursuit of saving Madoka. Like. C'mon. You're the viewer, isn't it a little pathetic to fall for the facade she puts up? Think about how hard she tries to talk Mami into cooperation, how she tries to prevent Sayaka and Kyoko's feuding, how she is the literal last one to resort to violence among the magical girls in the TV show loop. Even her threat to kill Sayaka only comes when Sayaka is on the verge of transformation, and only after Sayaka refuses all help to avoid her own death in the first place.
I guess all I'm trying to get at with this one is like... Homura isn't ruthless. She's not even particularly violent. She cares about her friends. She doesn't want to hurt them. And, unlike Madoka, I'm not sure she even has the stomach to truly hurt them if it came down to it.
I've got plenty more homura thoughts, of course, and if you're a fan of that sort of thing, I've got quite a few fics with her as the PoV or love interest on Ao3. She's a fun gal.