Alyssa Rosenberg says that Captain America: The First Avenger's portrayal of institutional sexism wasn't all that:
My assumption was those doors were British ones — Peggy is, after all, a U.K. transplant to an American unit. And it’s true that Col. Chester Phillips can be skeptical of Peggy’s judgement out in the field as part of a larger skepticism of what Cap, who up until his arrival in Europe has been a war bond-shilling show pony, can actually accomplish that’s of military value. But she’s entirely accepted as a partner by Howard Stark and Dr. Abraham Erskine, and she gets to shuck that pencil skirt and put on some pants to fight Hydra on the ground. (Erskine’s top secret lab is guarded by a lady with a shotgun, too.)
In a sense, that fact that Peggy gets to hit the front lines and defend her man is just as cheery and dismissive of actual history as the suggestion that World War II units were racially integrated. Women in both the WACS and the WAVES were kept out of combat (something that actually occasioned prejudice from men who thought they’d be taken out of combat and sent to the front lines), and the WAVES were confined to the continental U.S. and Hawaii. The names of both units signaled that they were meant to be temporary units rather than to pave the way for women’s long-term service in the military. Somebody may have shut a door on Peggy Carter somewhere, but in Captain America, it sure wasn’t the U.S. Army.
Well, I don't know about that. It really didn't occur to me that Carter was referring to institutional sexism in the UK -- if I remember correctly, she says that in the context of empathizing with Steve Rogers' numerous failed attempts to enlist, which suggests that she was talking about the U.S. Army.
I'd agree with Rosenberg's larger point that the film's portrayal of gender in the U.S. Armed Forces during World War II isn't particularly realistic, but it was certainly more so than it's portrayal of race. The old woman guarding the secret lab is presumably an OSS spook. The other women in the film are shown doing clerical work not performing combat roles, when they're not dancing in Cap's troupe.
I don't think I buy Rosenberg's larger point about the contrast between the Avengers and X-Men films as one of institutional optimism vs. institutional failure. The primary villain in the Iron Man films is the military industrial complex: In the first film, Obadiah Stane's greed leads him to sell weapons to America's enemies, while in the second film, Tony Stark only narrowly averts a civilian massacre caused by the military's theft of his armor and its collaboration with unscrupulous contractor Justin Hammer. The Incredible Hulk's nemesis is a rogue general who is obsessed with capturing Bruce Banner so he can field an army of gamma-charged monsters. Thor features a clueless national-security establishment appropriating Jane Foster's research PATRIOT Act style, and it ends with her former partner offering advice to S.H.I.E.L.D about the cosmic cube while under Loki's influence. Only The First Avenger really exudes institutional optimism, appropriate for the era of the Greatest Generation and the New Deal.
All of Marvel's films really have something in common--like comic books in general, they all mostly reflect liberal political sensibilities (not partisan, but liberal), even when they choose to criticize government. But look at it this way, conservatives, you'll always have Fables. Well, neoconservatives anyway.