Not how we’re wired, how patriarchy views both forms. Seriously, you can’t just put up a study that confirms an assumption of patriarchy without acknowledging that it is, on some level, circular logic.

This is a wonderful idea, it's not a falsifiable theory though. This makes assumptions that Patriarchy in its current form is so deeply ingrained it affects every study on nudity preferences done at the subconscious level. So the only way your idea could ever be proven is if we, in a vacuum, develop cloned humans and developed a specific matriarchal society for them that we some how teach them without any possible contamination, and then repeat tests like these and see if there's a difference.

Patriarchy is the dominant worldview, patriarchy says that beauty is a feminine trait, most people agree that women are more beautiful than men. All that proves is that most people accept the patriarchal definition of beauty.

Or alternatively, Patriarchy developed from common human traits in majority, which resulted in a preference for the female form in regards to beauty (it didn't), which associated beauty as a feminine trait (it didn't), and thus it's not the tail that wags the dog, but indeed the opposite.

If you conducted this same study in ancient Greece, would you expect the same result? If no, then cultural views of beauty play a big role in this. If yes, then why were the ancient Greeks obsessed with male nudity?

Yes, actually. And more specifically it would benefit your argument if that study was done -- since Ancient Greece was a heavily patriarchal society regardless of which period you pick and which society you want to pick within Ancient Greece. Arguably it was a more patriarchal society than today; with the fact women were not seen as sexual partners (Athens, Sparta, etc), just spouses meant to produce children.

We'd also have to broach the fact that outside a few renaissance artists imitating an ignorant variance of ancient Greece, there was not an obsession with male nudity over female nudity. They were just more open with both compared to later western societies that built themselves with Greece as a template.