Overall, does The Great Gatsby challenge or reinforce traditional femininity and masculinity?
The novel supports traditional masculinity. The freedom the females seem to have in the novel is an illusion.
There's not a round, developed, complex female character in the entire novel. All the women characters are sirens who tempt men. The women are trophy wives, materialistic mistresses, cheats, and fools.
Referring to her daughter, Daisy admits:
I hope she'll be a fool - that's the best thing a girl can be in this world, a beautiful little fool....You see, I think everything's terrible anyhow....And I know. I've been everywhere and seen everything and done everything.
Jordan is a "a device to bring Nick Carraway into the plot." She is as careless as the day is long. She cheats at golf. Her conversations are full of gossip. Nick says to her:
Suppose you met somebody as careless as yourself.
Myrtle cares more about possessions (suits, dog collars)than about human feelings. She says this of her husband:
I thought he knew something about breeding, but he wasn’t fit to lick my shoe...He borrowed somebody’s best suit to get married in, and never even told me about it, and the man came after it one day when he was out. ‘oh, is that your suit?’ I said. ‘this is the first I ever heard about it.’ But I gave it to him and then I lay down and cried to beat the band all afternoon.
After Myrtle says "Daisy! Daisy! Daisy!" Tom slaps her, the way he might punish her dog for barking. That's symbolic of the intentionally flat female characterization in the novel. So says Enotes:
Daisy, Jordan, and Myrtle exist in relationship to their husbands, lovers, or boyfriends, and none undergoes a significant change during the course of the narrative. Thus, according to the most common definitions of flat versus round characters in literature, none of the women can be considered “round” or multidimensional characters. Each functions—at least for a time—as the cynosure of Gatsby, Nick and Tom Buchanan.
Fitzgerald certainly challenges traditional roles throughout Gatsby. Many of the male characters--particularly Tom--are portrayed to be brutally physical and overbearing toward the females in their lives. However, these examples and behaviors are not glorifying these relationships but rather drawing them in question, challenging readers to think beyond these stereotypical male roles and the unhappy relationships they produce. Likewise, many of the females--Daisy and particularly Jordan--within the story also challenge tradition as they exert their own will and desires both in their personal relationships and in their interactions with the larger world as a whole.