We've already accepted as a society that some technologies are too big and dangerous for private individuals to have access to, for the sheer pragmatic reason that there are people crazy enough to do literally anything. Technology that allows a single human to kill every other human on Earth is a really good candidate for restriction. Biohacking is such technology. It's real-life nanobots.
Another good example is how you can't photocopy money. Did that stop counterfeiting... no. but it sure did tamp down a lot of casual counterfeiting - and i don't think it actually did harm people's liberty very much.
Furthermore, there is a clear difference between “you can’t do this to other people” and “you can’t do X or Y to your own body”, the latter of which is at play here. Photocopying money, selling dangerous medicine, and spamming the radio waves with noise actually affects other people. Personal experimentation with mRNA does not.
Regulating mass market mRNA products before they can be sold? Sure. Banning individual experimentation? Hell no.
I’d argue that the only way to put that many genies back into their bottles is an authoritarian government, which is never worth it no matter what promises a would be tyrant makes.