What I take to be elementary significant papers on this question pre-date arXiv, so they are unfortunately usually available only behind paywalls. I've always found the simplicity of Willem de Muynck's argument in Physics Letters A 114, 65 (1986), "THE BELL INEQUALITIES AND THEIR IRRELEVANCE TO THE PROBLEM OF LOCALITY IN QUANTUM MECHANICS", somewhat compelling. I can reproduce the basic argument here under fair use, from the first page,
In his original derivation Bell 3
assumed his hidden variables theory to
satisfy a locality condition which he
deemed to be a"vital assumption".
Presumably due to this fact there
still exists a widespread belief- also
among specialists - that the Bell
inequalities can not be derived for
nonlocal hidden variables theories.
This would leave open the possibility
that quantum mechanics might be
reproduced by a nonlocal hidden
variables theory. From the following,
however, it should be clear that the
mere existence of hidden variables is
sufficient to yield the Bell
inequalities. Hence not only local but
also nonlocal hidden variables
theories are incompatible with quantum
mechanics. Local and nonlocal theories
being on an equal footing it also
follows that the Bell inequalities are
completely irrelevant to the problem
of (non)-locality in hidden variables
theories. (my emphasis here)
After I extracted the above, I found a PDF of the paper on de Muynck's web-page, I'm pleased to say (it's elementary math, and only 4 pages). A similar but rather more algebraic construction, which I think is mathematically quite a bit nicer, can be found in Lawrence J. Landau, Physics Letters A 120, 54, 1987, "ON THE VIOLATION OF BELL'S INEQUALITY IN QUANTUM THEORY", without, however, making anything like de Muynck's claim for its significance (I don't believe it, but I found it here). IMO, this simple algebra underlies the question of locality/nonlocality to this day -- one takes this argument seriously, or one does not.
Ultimately, locality is very closely tied to measurement compatibility because measurement compatibility is required for measurements that are at space-like separation in quantum field theory. The implication does not apply in reverse, however, so space-like separation of measurements is not equivalent to measurement compatibility.
The spanner in the works, a big one, is that measurement compatibility (and hence by implication space-like separation) does not imply no-correlation. There are correlations at space-like separation in quantum (field) theory, but one can prove (I realize here that I don't know precisely what additional assumptions are needed, but conventional QM frameworks are enough) that one can't use those correlations to send messages.
I have to point out that you shouldn't take too much for granted your parenthetical comment "(I assume I understand this one)". If you look at the other Answers here, you'll see that locality is far from simple. I particularly draw your attention to sb1's introduction of "influence" as part of his last paragraph's discussion, which I suggest is not simple at all.
It's important, IMO, to understand that this argument has been gradually changing over the last 50 years. It's not clear when or whether a novel argument will appear that makes it worthwhile to think in terms outside quantum (field) theory for practical purposes, but novel arguments are constantly emerging. The fact that Michael J. W. Hall (cited by Jim Graber above) has managed to publish his novel argument in Physics Review Letters is enormously impressive, particularly when one sees the robust tone he adopts, because PRL sets the bar very high indeed for foundations papers, but time will tell whether the argument can be used constructively in a quantum field theory context.
Finally, reading through my Answer, I realize that it does not directly address "realism" and "contextuality". That's because I associate mutual measurement compatibility of all observables directly with classical realism, all measurements commute, and the sometime presence of measurement incompatibility with contextuality. Measurements may have an "influence" (hee!) on some other measurements, and not on others. I might expand on this already overlong Answer later.