The von Neumann-Morgenstern theorem has nothing to do with utilitarianism, and it's not about what you "should" do.

Agreed, unfortunately a lot of people around here seem to interpret it this way.

In particular, it can prefer fair outcomes to unfair outcomes for any definition of "fair".

I would argue that fairness is a property of a process rather than an outcome, e.g., a kangaroo court doesn't become "fair" just because it happens to reach the same verdict a fair trial would have.