I thought it would be
(theory of) evolution
Explanation as per request:
I know what is or isn't, but never what might be;
the results at one point of the process of evolution are a given, but only a theoretical all-knowing entity (Laplace's Demon) could accurately predict what evolution will lead to in the future. Added later: forgot my most compelling point here. Evolution itself does not (need to) look forward to function. There is no planning or looking ahead, just basic rules that always apply and will lead to the desired result (in the long term)
And many claim to know me, though many disagree;
This one is fairly straight-forward: many people claim to know (understand) evolution, and claim that it is a fact. However, many people also disagree (often proposing intelligent design instead).
There are no sly dilemmas, no subtleties I see;
Evolution is not about morality, and in a sense is a fairly simple, straight-forward process (though the results that emerge certainly aren't). That's what I thought of when reading "sly dilemmas" and "subtleties".
Both I encompass gladly, to be, and not to be.
Evolution is as much about 'succeeding' as 'failing'. The process of natural selection only works because each entity has strengths and weaknesses, which are only strengths and weaknesses in a given context. What turns out to be strong, will 'be'. What turns out to be overrun by the environment, will 'not be'. Both are necessary for evolution to function.
My explanation may not be perfect but hopefully the idea is clear.