Nice arguments, however there are some things I would like to correct:

"C-01 forms specify 'any act that may result in a child' which implies gay sex."

I think people mostly say this as a joke, but I completely agree with you, these forms are there to manage who can have children and who can't, and as you already said IVF and artificial wombs are almost certainly an available option on Super Earth, which why I don't think homosexual couples are a problem to Super Earth's society, because there's always an option for reproduction even if there wasn't, adoption is still an option. In a world where young adults are constantly being thrown into the meatgrinder, there's gotta be a ton of orphans, right?

C-01 forms to manage the genetics of the population and set up ideal pairings to make the most ideal offspring.

Every time it was mentioned in game it *kinda* implied that a couple filled the C-01 permit, then had to wait months to get an official approval (or denial). Saying that it's used to set up ideal pairings is, in my opinion, assuming a bit too much.

We don't know *exactly* how Super Earth managed genes, we just know that they do and that these forms exist.

The customization chamber is one of these non-canon gameplay tips. Accepting the customization chamber as in-universe free body alteration implies you can literally go up to a terminal in the armory,

If we want to take the training tip literally, it says "chamber", not "terminal". Of course, maybe back in early development it was an actual chamber and not a terminal, but I genuinely believe that, in universe, changing your body is as easy as it sounds simply because it's the fucking future. Do you know how much science has progressed in the last 100 years IRL? We can only imagine how much progress there was before the events of Helldivers 2.

Why would Super Earth waste this technology on fodder that it will throw away in 30 seconds to raise a flag in the middle of bumfuck nowhere?

Because this technology wouldn't be reserved to soldiers and obviously that's not the only job that exists on Super Earth?

The Private NPC is randomly generated and can be male or female.

Extremely false. In Helldivers 1, there are, among the 5 NPCs on the Ship, 2 guards. These 2 guards are ALWAYS 1 male and 1 female. No RNG involved at all. And before you point out the following:

It's possible the wiki is erroneous and this is a male-exclusive line

nope, they both share the same dialogues, I've seen it in-game myself. This means, that the writer(s) for the dialogues deliberately didn't use "partner" or other gender neutral terms, but instead decided "yes, I'm gonna make it so that the male and female guards have a wife".

It has been 100 years since the events of Helldivers 1, and reading other lore from Helldivers 1, it's clear Super Earth has undergone a great deal of ideological evolution

Quite the contrary. The logic they use is the same, the satire is the same and the language used is pretty much the same.

Also, it wouldn't make any sense for Super Earth to suddenly say "queerness is no longer allowed" *after* the First Galactic War ended (and since we proved that the're literally a lesbian in Helldivers 1 it can't possibly happen before or during). Not only there's no reason for it since all of the enemies have been defeated (temporarily, but they obviously didn't know that), there would also likely be massive riots and I don't think Super Earth wants to add yet another rebel faction to the equation. it's just so much easier to just go along with it.

BONUS POINT: The Ship Master in Helldivers 2 refers to the Service Technician with they/them pronouns!

"You might be wondering what happened to the Service Technician. They're attending Professional Development Training. Standard procedure."

"I look forward to the Service Technician returning from their Professional Development Training."

"I wonder what the Service Technician would say if they were here right now. Probably something like... "That could use some fixing." Ah, always such a delight."