When those ideas were injected into the movement so early in its history, was it coopted by bad actors or actively shaped by them?
It's true that Dworkin wasn't anti-trans, even if the transphobic ideas of her time seep into her work, as we see in the paternalistic attitude present in this passage. However, we have a few years, a decade at best, of radical feminism being trans-ambivalent before terfism became a prominent part of the movement. And that's gone on for almost five decades. Even with the current terf-feminist divorce of the last decade, prominent contemporary authors that identify as radfem, such as Amelia Valcárcel, are quite transphobic.
Compare that to intersectional feminism. Even if Hooks' foundational Feminist Theory contains questionable elements in her argumentation (like saying, or at least implying that gays and lesbians don't suffer systemic oppression), she herself revised those ideas in later works and later trans feminist authors got grandmothered into the current.
I'm referring precisely to figures like Joyce and Rowling when I talk about the "terf-feminist divorce". I agree that the modern "gender critical" individuals have little to do with feminists, and they themselves are moving away from the classic moniker too. But as a movement, I'm aiming for just the contrary, underlining the "feminist" in terf. remembering that terf stems from feminism points a finger at the failures of white, straight, upper-middle class feminism. I think it leads to much more useful discussion than trying to restrict a movement to its foundational authors and texts.