For a professional writer you'd think she would know that a quotation (even a fictional one) requires quotation marks around it to make it clear to the reader that it's not what you are saying but somebody else. Perhaps this makes more sense:

"Refusing to accept that people who don't like sex belong in the gay category is akin to wanting segregated bathrooms in the 1950s, John," as approximately a thousand gender activists will inform you once their hands stop literally shaking.

She's mocking the people who replied to her.

[–] Semi_Hemi_Demigod@lemmy.world 10 points 20 hours ago

Wow she really isn’t very good.

How were we so starved for something that we latched onto her baloney?

[–] Stillwater@sh.itjust.works 4 points 20 hours ago

I don't read it like a quote. She's telling John an opinion (sarcastically) and then letting him know the activists will inform him the same thing. It's not grammatically incorrect, just difficult to parse (which is still not the best writing).