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“This above all; to thine own self be true, and it must follow, as the night the day, thou canst not then be false to any man.” – Hamlet
True words, as it is hard to be false to the world when we are true to ourselves. When we experience many back stabs in the course of our lives, we might tend to become a bit skeptical about trusting people; however, this is not the way to live fully, as it denies the essence of Love. By being true to yourself and putting out the best of you, the ball ends up on the other’s court – even when you experience deceit, you are at peace with yourself. In this world, the good and the bad coexists, and sometimes, wolves wear sheep’s attire – the only weapon against that is the satisfaction of being true to yourself.
Inkspeare 
This quote comes at the end of a parodic series of sententious banalities and from the mouth of the untrustworthy, witless toady Polonius. Claudius in this play murders his brother in order to remain true to his ambition. Iago in Othello and Edmund in King Lear both express their intentions to remain true to their own natures by playing everyone else false. Shakespeare was far to smart to think that something so trite was true.
Whether you are a saint or the devil, there is no denying of the self, to remain true to your self (whatever that may be at a particular stage of life, as we evolve as creatures) is the only thing left. This is an interesting topic, as it can go on an on – We can ask this question – Is a serial killer being true to the self? What about a person with multiple personalities? Or is it just a decay or corruption of the self? As you point out, Shakespeare was too smart.
You’re probably better off being true to something outside the self especially given that the self is an illusion. This seems to be the broad message of rather a lot of major religions and philosophical systems throughout history. (Shakespeare didn’t really have a message I don’t think.)
N.B. Creatures don’t evolve, species do.
Whether Shakespeare had a message or not we’ll never know for sure. I guess one takes from his writings what one wants or needs. In my case, I consider myself a Christian, a spiritual person, and open minded to others beliefs, so I would take from it, I guess, from my context. Other people will find something else, but that is the beauty of it – something for everyone, and maybe the intention behind it. I believe that we evolve – in the sense of beliefs and thinking – as our experiences broaden in the course of our existence. Today, that quote means something, in the future, who knows, maybe the same, more, or less, or maybe nothing at all ???
People can indeed take different meanings from the plays. Coriolanus was, if memory serves, performed in the 1930s in France and Germany. In the former it was agitprop for the radical left, in the latter propaganda for the Nazis.
This quote, however, taken from its context in the play is illogical and possibly rather dangerous in its solipsism. (The fact that night follows day rather than the other way round, ie light leads to darkness, might be a suggestion of how we should take the argument.) The whole play might be seen as Hamlet attempting to grapple with what it means to be true to one’s self. As a Christian you might see that Lucifer was true to his own self. I imagine though that most saints would consider themselves as being true to Christ rather than themselves.
Excellent points made on Lucifer and the Saints.