I don't see how anyone could consider it not a parody. I mean the main character himself is named Hiro Protagonist (a pun on the literary term "Hero Protagonist") and Hong Kong exists as a chain franchise nation.
You can’t watch “Are We the Baddies?” as a war story. It introduced such elements simply to establish who’s getting made fun of. They remain in character but that’s it, the war story plot doesn’t progress the skit just keeps hammering the parody. Some parody has a more complete story but “Scary Movie” progresses the underlying plot to make fun of different elements of the movies it’s making fun of.
Harry Potter on the other hand calls out many of the tropes it’s using. House of the lions vs house of the snakes, guess who’s supposed to be the hero and who the villain. Except the characters once introduced are telling an actual story.
Snow Crash is between those extremes but focuses too much on the underlying story and its characters to be an actual parody. Over the top elements exist in the world, but they are played straight more Gulliver's Travels than Spaceballs.
I feel like snow crash it's kinda along those lines.
I think where NGE really shines is the art, design, animation, which are all stunning. I have much respect for NGE, but specifically as a deconstruction of the mecha genre I've never been impressed.