I don't know anything about Minnesota, but wrt this referendum and the last UK General Election it wasn't so much "picking a winner" as that relentless vilification of the non-establishment side led to people concealing their actual voting intentions from pollsters. In the case of the GE this even applied to exit polling, i.e. after people had voted. There wasn't any official exit polling for the referendum, but some major banks did it privately and I think Leave's premature concession early in the results points to the same thing happening there.
Thank you for a very thoughtful and measured post, by the way; we could do with more of that. The atmosphere here in the UK at the moment is just poisonous, with some fairly mortifying behaviour on both sides.