Tommy Wonder had a fantastic psychological way of dealing with this.
First way, was VERY simple and overlooked.
Don't pose it as a puzzle.
This means it is not about showing how clever you are and becoming an intellectual challenge. It seems obvious, doesn't it? But in my experience the magic society is as feeble and conformist as any, and magicians tend to vehemently advocate sensible ideologies but turn out to be some of the biggest hypocrites I have come across since Jingoist America.
If you agree with Tommy Wonder on that, then you have to actually make a change in what your doing in accordance to that belief. Just saying it and nodding along, won't help anything. Mini-rant officially over now.
This is, in my opinion, one of the big things to consider in magic theory and Tommy summed it up much better than I can:
'If you can transport people out of the role of detective or, better yet, prevent them from entering into that role- you will have done them a good service, since you can offer them something of much greater interest'
However, Tommy agreed that even if you were being charming, likeable, entertaining e.t.c. there were still going to be some people who had the psychological disposition to treat it as a puzzle and the threat of anything affiliated with deception leads them to feel socially obliged to demonstrate their intellectual erudite by rejecting the magic.
His initial response to this was to involve the spectator in some way. If the spectator is sat eyes-glued to hands then he would get them participating in some way, which psychologically took down the barrier they had erected in trying to remain distanced and disassociated from the performance.
He was also an expert at using social pressure to elicit a desired response from a trouble maker. He avoided confrontations and challenges with the spectator directly, so rather than show the spectator that they are wrong about a method, he would ingeniously show everyone else, but the spectator, that he was wrong. This meant that he had proven the spectator wrong to everyone else and there was inherent social pressure.
I could go on all day at Tommy's ingenuity- but I don't want to spoil it for anyone. Learn everything you can about the man, the guy was an absolute legend.