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.

Not to defend her, but she's saying that the ""woke"" crowd is saying what she's saying is as bigoted as segregated bathrooms. She's racist for entirely independent reasons