Eesh...the moral part is something that I firmly appreciate pretty much entirely avoiding.
Yes, there are areas where chemistry and morality can overlap, but those are areas that I tend to skirt. I tell the story of Fritz Haber developing chemical weapons for the German government during World War I and his wife eventually killing herself, not being able to live with her indirect involvement. I tell the story of Neils Bohr having to dissolve his Nobel Prize in aqua regia before the Nazi's took Copenhagen. I also relate very tangentially the decisions that had to be made by chemists/physicists in taking part in the Manhattan Project.
These are direct, dramatic examples where chemists have had to make choices of whether to continue with research or to turn away. (Well, the Bohr story isn't, but it's just freaking cool.) In each case, knowledge won out over possibly more moral choices. In the long run the philosophy of science says that the pursuit of knowledge is, of itself, the highest pursuit. Nothing else tops that, and how that knowledge is used is almost always of secondary concern.
I do discuss environmental concerns, and those are - to me - moral concerns. We discuss what should and shouldn't go down the drains and why. We discuss why we should or shouldn't pursue nuclear power. We discuss the greenhouse effect. Those seem natural connections to chemistry education for me.
It also means pointing out that even though most of the scientists we study are white men there were many others involved in the discovery of some of our concepts - Nagaoka theorizing the existence of the atomic nucleus, Meitner and Curie helping discover elements and radioactivity, the research currently ongoing in India, Japan, China, and many other countries.
I don't do a lot of moral teaching, I don't think. Partially because I don't always feel comfortable doing it, and partially because it often feels forced to include it in chemistry.