I have been team leader my whole adult life (CEO of a small company for a decade, and now director of a division of a bigger company).
I am autistic myself.
And I am horrified to see this antivax (and anti-science in general) thing happening.
Yet, if someone were to tell me "it's me or her", whatever what I think of the two persons, the only answer would be "then, sorry, you'll be missed".
You can't appear to be blackmailing and using resignation threat.
You can't make it a personal matter. And that is what you are doing. You didn't say "I want her to stop that", you said "I want her gone". You can't.
So, my advice would be not to focus on the person, but on what she says.
Tell your leader how you feel about antivax speech in the workplace.
Tell your leader that you believe that it gives a retrograde image of your company to allows anti-science.
Tell your leader that you don't accept your disorder to be discussed and used as an argument.
And if you really want to go "resignation threat", tell your leader that you can't work in an environment where antivax theories are spread, and even more, where your disorder is used to spread those theories.
But it is not your place to tell that the only acceptable solution is her gone.
Let your leader figure out what is the solution.
He/she will probably tell her to stop doing that (if he/she doesn't, then you can go back to resignation threat).
And if she doesn't stop it, then it will also become your leader problem (his/her instructions were ignored).
Bottom line: you don't want to be the intransigent one, by saying that there is no way out (outside firing her). Just say why it is bad for the company and for you. And let your leader try to find a way out; and your coworker to be the intransigent one if she doesn't accept to change her behaviour. Intransigent one are those who get fired.