Given that SKU is all about fucking gender roles up where the sun shineth not, misogyny is a running theme in the series. But I'm just wondering, how much of it is genuine, violent and overt misogyny as opposed to a deconstruction?

It's the lasses of SKU who appear to get hurt the most. Saionji beats the shit out of Anthy. Anthy responds with a great deal of subtle malice, but it's nothing on the level that she extends to Nanami. Touga manipulates and uses the fuck out of everyone, but by far and away the majority of his victims are women. Likewise Akio; he also plays everyone around him like a violin, but he reserves outright torture and mental destruction for Kanae, Utena, and at some point Anthy well, as at one point he basically coerces sex from her when she is reluctant. And towards the end of the series it's hinted (via Anthy's facial expressions and body language) that this reluctance continues through the series. Juri appears to get off comparatively lightly, but frankly she has even more masculine traits than any other female character. And even some male characters. (I'm looking at you, Miki.) Akio tortures Kanae in many different ways, but even though he plays Mikage like a violin, it really isn't the same level of 'fuck you bitch' that he extends to Kanae.

So, the question arises: do the women of the series suffer more because their gender roles make them vulnerable, or are the male characters specifically targeting them because they're female?

It's a subtle distinction, but I think it's an important one.