During my recent visit to Oxford I had occasion to talk to many philosophers who do applied ethics, and who do meta-ethics. They confirmed for me these two facts:
Applied ethicists pursue their work, trying to coordinate views on specific moral conclusions and general moral principles, as if there were no study of meta-ethics or moral psychology.
Meta-ethicists, and also I presume moral psychologists, see their work as quite relevant for the applied ethics.
These two communities thus seem to disagree on the relevance of meta-ethics (and probably also moral psychology) to applied ethics. This disagreement could be attributed to bias on either side – to increase their autonomy and importance, academic fields may well be biased to see other fields as less relevant to theirs, and to see theirs as more relevant for others. But as usual in a dispute, at least one of these communities must be very wrong.
Guy, I'll accept that "normative ethics" may better describe what I meant that "applied ethics." You seem to me to be saying:1) The meta-ethicists I talked to who said normative ethicist should respond more to meta-ethics are not representative.2) At present normative ethics should in fact be practiced "as if there were no study of meta-ethics or moral psychology." Or since "the connections are rather complicated" you can't identify any particular way in which they should respond.
My impression as an amateur is that we can identify particular ways which in which normative ethics should respond; I guess I'll have to query meta-ethicists and moral psychologists in more detail about this if/when I get the chance again.
Robin, I think the opposing views you're ascribing to metaethicists and applied ethicists are far too vague. I doubt any serious philosophers working in these two fields (and there are enough, though not many, who have done work in both) would subscribe to them. So it's very hard to assess whether this supposed disagreement exists. I think your impression is mistaken and there is no significant disagreement here.
Since this is a very big topic, my comments will have to be very broad.
(1) The division between meta-ethics and applied ethics is a bit misleading. A very large area lies in between the two: normative ethics. Applied ethicists are certainly intensely interested in what goes on there, so the real question is whether normative ethicists are interested in what goes on in meta-ethics. The answer, very roughly, is that they are quite interested in some of it -- say in epistemic questions about methodology. Less so in questions about semantics and objectivity.
(2) But I'd say that it's metaethicists who tell them that these questions either don't have relevance, or at best have very indirect relevance, to the practice of ethics. Indeed the very distinction between meta-ethics and and normative ethics is the distinction between questions about the nature of moral facts or the meaning of moral statement and which moral claims are true or correct. Most meta-ethicists tend to be rather impatient with people who think that if objectivism is false then everything is permitted, or morality is undermined, or relativism is true, and so forth. None of these things follow. Nor do any substantive consequences for the major disputes within normative ethics -- e.g. that between consequentialists and Kantians. The fact that someone is an expressivist or subjectivist or naturalist or fictionalist doesn't tell you anything about their substantive views.
(3) By meta-ethics you seem to mean epistemological questions, and in particular the question of scepticism (I'm not sure you're distinguishing moral scepticism and moral nihilism, very different views). These, while hardly ignored, are not at the heart of meta-ethics and, as I suggested, they are not simply ignored by normative ethicists. But even here the connections are rather complicated. Scientists don't stop their research because there is as of yet no conclusive solution to scepticism about the external world.
(4) 'Moral psychology' can mean (at least) two different things: an area of philosophy falling roughly between philosophy of mind and ethics (the area, for example, where questions about freedom of the will and resposibility are discussed), or a certain area of empirical psychology. I suspect you mean the second. Again it's hard to make any sweeping claims. Some of the relevant empirical work here is fairly recent, and its philosophical implications -- for either meta-ethics or normative ethics -- is not yet very clear. I'd say that some applied ethicists are more likely to be overly impressed by the relevance some of this work, and that the job of meta-ethicists is rather to explain to them that they have misunderstood its relevance (non-philosophers are even more inclined to misunderstand the significance of this work).