MGS as a series has always had humorous elements to it. Cardboard box, magazines to distract soldiers, getting peed on, slipping on bird poop, crocodile helmet, shooting frogs, rolling around in a barrel, shooting a beehive to distract guards, I mean you're acting like this is the first game in the series to have 'humorous' elements. The chick hat serves a gameplay purpose of making it easier for players, which again isn't farfetched to the serious.
You cite the only lighthearted moment being the birthday scene. Well, there's the puppy scene, every scene ddog is in is pretty lighthearted, the burger tapes, the various joke tapes around the game(Some which serve a purpose, like informing a guard that you're dead or pooping), so no this game doesn't exist in a vacuum just because you say it is.
And the reason it isn't a 'perfect example of sexism' is because this thread exists and continues to exist. The fact that a discussion can spring from this and examples can be provided for both sides prove that it's more complicated than that. And it's funny you say I'm 'creating agency'. Then again all you have are .gifs out of context...so here, a scene from one of your gifs. Quiet takes control of the situation, makes Snake follow her.
https://youtu.be/T-W8oeK5YVc?t=33s
But of course your gif only has the bit with her ass after it. No, there is Quiet displaying agency and taking control of the situation instead of letting ocelot shower snake with a bucket. That is one of the many moments where she displays agency(The other one again, trying to kill you in the beginning).
That is a form of agency, whether you like it or not. That is Quiet doing something not told by you, but written to do that yes(As is every other female character in every other game before we go down that slippery slope) but still a form of agency displayed by her.