Replace "black man" with "white man" and "stupid woman" with "stupid man". The statements sound a bit odd now, because there is a subtle form of discrimination in the original form. We can even make the "white man" form sound racist if we imagine it came from a Japanese man living in his home country.
The tendency to describe the mugger as just "black", rather than making a more accurate description such as "tall/short, slim/well-built, black man" , shows repressed racism. Similarly, William Hague could have just used the word "stupid" and the message would've been the same. He added the word "woman" due to his repressed sexism.
Regarding the OP, mentioning that his neighbours are "ethnics" has no bearing on his report so, again, xenophobia or racism are lurking around the corner.
I don't agree that replacing "white" with "black" and "man" for "woman" make those statements sound particularly odd, nor do I agree they highlight a discrimatory element to the originals.
You're right in saying Hague could have merely used the word "stupid" without referring to Jamieson's gender, but it's a bit of a leap to say that the inclusion of "woman" points to repressed sexism. If a kid does/says something silly, they're often called a "stupid boy" or "stupid girl" so why shouldn't the same rule apply to adults?
As for the mugging scenario, alluding to the mugger's ethnicity could be completely innocent and mentioned purely to offer greater description of the asailant. You're not saying the mugger's ethnicity was the reason he/she mugged you, you're just recognisisng it as a distinguishing feature.
I really do wonder why some people go to such lengths to shy away from all mention of race, as though it's completely taboo regardless of context. What are you afraid of exactly?