Here is a brief explanation of Street's constructivism as I understand it, and the main problem I see with it (apart from a number of errors in the arguments, but that's not central). I recommend the papers if anyone is interested - I'm not an expert on her theory, and I haven't read it in a while in detail. Still, I think I got the gist of it.
Briefly, Street seems to conflate morality with rationality, though the error goes back to other prominent philosophers. She argues against the idea - which is common enough - that an agent A may have reasons that are not dependent on the evaluative attitudes of A, though not necessarily the present ones, but rather, what A would have in a situation of 'reflective equilibrium'. But she equates something like 'A has reasons to X' (or 'A has
overall reasons to X', though she often leaves that implicit) with 'A ought to X', and for the most part at least, she makes no distinction between 'all-things-considered' 'ought' and moral 'ought', though clearly she assumes that the 'all things considered' is a matter of rationality.
When one looks at it as a theory of rationality, it does seem to yield the right results:
When it comes to rationality, I would say it would be all-things-considered irrational of agent A to X if, given the information available to A (including processing capacity), it would be against A's final goals, ordered according to A's own evaluative attitudes (or preferences, in a general sense). Now Street's theory would say it would be irrational if and only if A in reflective equilibrium, aware of A's evaluative attitudes, would reckon that doing X would be irrational. That's kind of a weird way of saying it, and
I suspect it has the direction dependence wrong depending on how she construes reflective equilibrium (but I'm not sure how she construes it), but still, with a good characterization of reflective equilibrium that gives the right results (one of my worries is that it might end up being tautological, but that might not be a bug).
But with those caveats, I would not claim the theory gets the wrong results when it comes to all-things-considered means-to-end rationality. The problem seems to be for morality. To use one of her examples, this theory holds that whether 'Hitler was morally depraved' is true depends on what Hitler's own assessments would have been, in reflective equilibrium. Leaving aside the issue of whether Street gets the direction wrong, it may well be true that Hitler's infamous actions (e.g., to start WW2, to commit genocite) were
irrational on his part if and only if Hitler in reflective equilibrium would have reckoned so (I think something like that is true, though there is a risk it might be trivially true). But whether his actions were
immoral - and whether he was morally depraved - does not depend on that (further caveat, though: Street is considering all sorts of aliens with alien minds, and that would require further consideration).
However, all of the above says Street's metathics theory is
false. But it is a form of moral objectivism, in the usual sense of the word 'objective'. It is also a theory in which morality would be mind-independent, in one of the senses proposed in this thread. And to give an example,
https://philpapers.org/rec/WARDMM
A central feature of ordinary moral thought is that moral judgment is mind-independent in the following sense: judging something to be morally wrong does not thereby make it morally wrong. To deny this would be to accept a form of subjectivism.
One could nitpick (how about judging something morally praiseworthy? etc.), but that gets pretty close to another sense of mind-independence, according to which Street's theory would make morality clearly a mind-independent matter.