Compatibilists: free will is a term for something real that we do.
Incompatibilists: no, that thing is trivial and should have a different name. Free will is a term for something impossible. But despite being impossible it's a meaningful concept. And it's somehow hugely important and deserves a name.
I'm unclear about the motivation for this, especially the last part.
My specific issue is with moral responsibility, which I believe is out of one's control. (So for example I don't think developers are to morally blame for writing bad code.)
Blame is a messy idea. I'm big on morality, it's how we know what to do next - what we should do, and "should" is a word indicating that a moral idea follows. Without morality I'd be (even more) like a sessile sponge, incapable of action. "Why bother?" is a moral question.
So one can say "I should do XYZ", but this soon descends into blame: "hey you, why didn't you do XYZ?", and that can be mean-spirited recrimination to do with bullying and social pressure, coercion and guilt and labelling people as no good, and main function of the question might not be to seek an answer.
Or, more rarely, it might be an honest enquiry into philosophical differences, or practical problems. Developers shouldn't write bad code. But they do, so we can "blame" them for it. That doesn't mean we should hurl rotten vegetables at most of them. On Wikipedia, I routinely blame people for fucking up an article, but the objective isn't to make them feel bad, it's to fix the article (and to check their reasons, to make sure that I'm not the one with the bad idea). Blame is one thing, but what to do with blame is a separate question.
It's definitely about the way people function, though, about enquiring into their mistakes and motivations. They have "responsibility" in the sense of being expected to respond to "why did you do XYZ?", and even if the answer is "it was inevitable because of the way I am", there's still more practical aspects of the answer ("because I was sleepy, because I was trying to avoid PQR, because I like XYZ") in which to seek knowledge. If we're all autonoma, so what: these autonoma want to solve moral problems.
Historically, ideas of "moral responsibility" are strongly linked with retributive punishment.
If you did something wrong, and you are morally responsible for it, then we are morally permitted (or even obliged) to make you suffer for it (where "suffer" can mean potentially anything from mild social opprobrium up to torture and execution). If you did something wrong, but (for whatever reason) lack moral responsibility for it, then it is morally wrong for us to make you suffer for it. If your moral responsibility is impaired but not completely absent, then it is wrong for us to make you suffer to the normal degree, but it might be justifiable for us to do so to a more limited degree.
But, many people today reject the idea of retributive punishment. And if you do so, it isn't clear how important the concept of "moral responsibility" still is. It is a logically coherent position to accept the evaluative/axiological aspects of morality (the labelling of states of affairs as "good" or "evil" or "neutral", their ranking as greater or lesser goods/evils), and its prescriptive aspects (you ought to do this, you ought not do that, you may do this but you aren't obliged to), while rejecting the concept of "moral responsibility" as misconceived, useless, harmful and/or erroneous.
Yes, but there again you are conflating three separate questions:
(1) Do we have choices?
(2) Are our choices "free"?
(3) Should we be held morally responsible for our choices?
How we answer (1) and (2) doesn't necessarily determine how we answer (3). And if (3) is your real point, maybe you should focus on that, rather than confusing things by conflating it with (1) and (2).
I don't identify as an incompatibilist, but to try to steelman their position:
Some incompatiblist determinists might view metaphysical libertarianism as a logically coherent possibility, albeit a false one. They might then view "free will" as useful in naming a way the universe coherently could have been, but turned out to actually not be – much like they might view Ptolemaic epicycles, phlogiston, the luminiferous aether, and steady state theory. And, much as a person might object to the position "the luminiferous aether is actually true, if we redefine all the terms involved to refer to concepts from special and general relativity" as a form of unhelpful obscurantism, they might view compatibilist determinism as doing the same kind of thing to metaphysically libertarian free will.
There's also the other kind of incompatibilism: metaphysical libertarianism is itself a form of incompatibilism. Both incompatibilist determinists and metaphysical libertarians agree that determinism and free will are incompatible. They just disagree on whether that means we should junk free will or junk determinism.
Although I think here "determinism" is a bit of a misnomer. Most physical determinists don't actually have a problem with the idea that there might be irreducible quantum indeterminism (whether or not they believe there actually is). An incompatibilist determinist would say "a clock doesn't have free will, and a roulette wheel doesn't either, so neither can some hybrid between the two". A compatibilist determinist will say that whether it is a clock or a roulette wheel or a hybrid of them, if it gets sufficiently complicated in the right ways, then it will have free will. For both, the real objection is to metaphysically libertarian ideas that human choice involves some irreducible "third thing" which is neither deterministic causation nor impersonal chance, nor any mere combination of the two. There are also claims (e.g. by Roger Penrose) that quantum indeterminism operates in some special way within the human brain, different from how it operates normally, and that human free will is somehow rooted in that. Many "determinists" (whether compatibilist or incompatibilist) would view that as uncomfortably close to metaphysical libertarianism, even if it does attempt to partly replace the transcendental metaphysics with something closer to the realm of the empirically testable (even if not quite there). But, while "quantum indeterminism operates in a very special way in the human brain" makes them uncomfortable, I don't think most of them view in the same way "quantum indeterminism is real and irreducible, but it doesn't operate in the human brain in any way differently from how it operates anywhere else"–again, whether or not they actually believe it. Some will prefer purely deterministic interpretations of quantum theory instead, such as many worlds or de Broglie–Bohm theory–but that debate has no inherent connection to the topic of human free will.
Compatibilists: free will is a term for something real that we do.
Incompatibilists: no, that thing is trivial and should have a different name. Free will is a term for something impossible. But despite being impossible it's a meaningful concept. And it's somehow hugely important and deserves a name.
I'm unclear about the motivation for this, especially the last part.