There is absolutely nothing fringe about wanting control of your body. This is a modern authoritarian take that is working to undo the last 50 years of increases in bodily freedom for everyone. I obviously won't win against someone espousing left-authoritarian views because neither of us will concede. But I do have some rhetorical things for you:
On "smoke and mirrors" for "an increasingly fringe, reactionary position". Do you think the same about abortion? Or is it, in your mind, okay for that form of bodily autonomy but some forms of bodily autonomy are more okay than others? Do you draw the line where "it harms people"? Who are "people"? It doesn't help you linked the CDC who has a vested interest in talking down the "bodily autonomy" argument as a public policy (public health is typically diametrically opposed to bodily autonomy because public health requires shirking the individual for the "common" good).
Arguing against bodily autonomy is binary. Either you are for bodily autonomy or you are for some level of government control over what people can and can't do with themselves. What I am willing to do to myself is my own business. Why should anyone but me decide?