Having come across the philosopher Sarah Sawyer online, I have come to think that her version of 'externalism' about concepts does not work for moral concepts because they incorporate value judgments, which empirical or mathematical concepts do not.
A good example is one Sawyer herself raises; the concept of equality which she includes in her list of moral concepts. But equality is sometimes a purely mathematical concept with no moral aspect at all. Even if I say men and women do not get equal pay for doing the same job, that in itself is a purely factual statement. It becomes moral when I say men and women should get equal pay for doing the same job. Equality is now linked with a value judgment which gives it moral force. I suggest the value judgment is incorporated into equality to specify situations where equality should (or should not) apply, whether it in fact applies at present or not.
It is probably unfortunate that a concept like equality, which in its mathematical aspect does come to us from the world as Sawyer says, needs us to add a value judgment which the outside world does not supply for us before it acquires moral force. The value judgments we add to concepts like equality we can also take away. Moreover, moral concepts can change their own subject matter whilst remaining moral concepts. That is illustrated by the historical argument put by Alasdair MacIntyre, broadly following Nietzsche, that the sort of characters and actions we called 'good' (in moral sense) in early Greek history changed later on, especially in Christian times.
Accordingly, I feel that Sawyer's attempt to show that we can maintain our moral ideas without worrying about particular moral beliefs does not work because moral beliefs are about what value judgments we should make both in general and in particular cases. She is trying to do something with concepts that has been tried at times from Plato onwards, but, sorry, I don't believe it works.