So, I already hold the opinion that 3H's writing is misogynistic in a lot of core areas, but it becomes very glaring considering its reflection in the fanbase, especially in one key example.
Edelgard and Rhea are meant to be narrative foils. How successful that attempt was on the basis of story writing and plot cohesion is one thing, but a less talked about aspect of that is how they're both played for fanservice. Direct opposites, if you will.
Edelgard starts the game as a child. Okay a teenager going on 18, but nonetheless she's young. That was made as part of her appeal.
Her initial mask is one of dignity and authority; viewed as a figure above petty nonsense and to be respected and followed. Break apart her shell, however, and you get the childishness. You get to creep on her sleeping, you get to share promises on a tower, she gets to whine to you about wanting to eat sweets instead of work, you get to make her blush when you praise her ideas, you can tease her about her scream when encountering a rat, you can walk in on her literally doodling your face on a piece of paper before she locks herself in her room for the following exploration phase.
In short, you get to be the one getting reactions out of her. You get to prod and tease. You get to dote and pull away her facade.
Now Rhea? She's the opposite. Like Edelgard, she too has a front of serene authority about her. She commands respect and reverence. But what do you get with Rhea when you bond with her? You get the mother figure.
Rhea's the one who dotes on you. She's doing the teasing, the prodding questions, the gentle reassurances, the compliments, and the ooey-gooey stuff.
Similar scenarios given how they're both fairly misogynistic depictions of strong women in an effort to get a male player to fall for them, but they're decisively different approaches. And nothing makes this clearer than fandom reaction.
Edelgard's childish, almost ingenue-like cuteness is seen as a facet of her character, one that's understood as not her entirety. Even if it's very explicitly reserved for Byleth, people are easily able to delude themselves into thinking that it could emerge with her other relationships.
But Rhea? She's only seen as this overbearing, controlling force. A creepy presence. Because she's the one doing the sweet talk.
A huge part of that is, of course, screen time and access to each character. Edelgard has a full support log with 10+ characters, Rhea only has Byleth. Edelgard is omnipresent in all routes, Rhea is MIA for most of 2 routes and flat out disappears in another. Byleth's (Your) first action is personally saving Edelgard from getting axed in the gut, while the first thing you know about Rhea is that she's untrustworthy per words of Jeralt.
There's intent behind this of course. Rhea is the red herring set up to be a tyrannical problem before re-railing into being the damsel in distress, while Edelgard the cute and sentimental gal you saved turns out to be an extremely violent imperialist. Obviously this was not that successful given the fanbase we see today. And part of that is that these very depictions are double edged swords.
People are not so easily swayed from first impressions. That includes the very makers of these stories, hence why Crimson Flower exists at all. They will see these intentional, calculated character choices and glue any and all future interpretations to them, hence why there's even more ushy-gushy Edelgard moments in CF and Rhea loses her sanity and becomes more erratic in speech. At that point, for a lot of people, it doesn't matter the context behind it, that it's clear that Edelgard's gap moe moments are bait for weirdos to be intentionally suckered in, and Rhea's trauma buttons are being constantly smashed, because you're in CF. It's a route where you abandoned moral convictions for what felt good at the moment despite all the evidence staring you in the face.
I could go on, like how I feel that a lot of people actually have some bad unchecked internalized misogyny regarding these differences between them. Another example is, despite Edelgard taking part in just as many, if not more, violent acts as Rhea (and to deeper degrees IMO), she can get away with it because she remains calm, collected, and measured. She remains pretty, even in her voice acting. Notice how Edelgard hardly ever screams or yells? Compare that to Rhea, who gets to wail and holler and roar? Rhea gets to have ugly moments, where composure is the last thing on her mind. That's uncomfortable, and it's not what's marketable for a woman character. And for most people, it doesn't matter how aware they are, they can still fall victim to being misogynistic, even unintentionally, when they hold one woman to a standard that they don't apply to another, with the key difference being in how they carry themselves.