There are lots of questions here related to the spin-statistics theorem, though none of them answer this question directly.
I had the notion that one can only prove the theorem on relativistic grounds and for example the Wikipedia page on the subject list Lorentz invariance as one of the assumptions needed to prove the theorem.
I got confused when I was reading Preskill's Lectures notes on quantum computation. He said on the subject:
All that is essential for a spin-statistics connection to hold is the existence of antiparticles. Special relativity is not an essential ingredient.
Then he proceeds to give an argument about why this is so. The argument is somewhat convincing, albeit a little hand-wavy.
Looking into the literature, there seem to be some back and forth arguments about this. For example see here, here, here, here, here, and here. So I have an idea as to where to start with this, however, I thought maybe I'm missing something obvious, and can save myself some time by asking here first.
Does one need relativity to proof the spin-statistics theorem? I'd also appreciate yes or no comments with reference to maybe later work on the subject that I might have missed.