Success!
It turns out that the census website lets you collate data online.
Below are two bookmarks, the first one for the Raleigh metro area, and the second for the Durham–Chapel Hill metro area. You will need to visit each one on a wide-screen device to view the table of data properly.
The specific data provided here are the count of women and men respectively, in different age groups, tabulated by ethnicity.
In the process of selecting the many tables to get these results, I lost track of when these data were last updated. I think some tables are newer than others. The web page says 2011–2015 but I am not convinced this is exactly correct.
There is a rule here in these forums that links to competitors are not permitted. Both the US Census Bureau and city-data.com provide a lot of the same data, so maybe they are competitors. Or maybe not, as city-data.com doesn't provide these specific data.
Raleigh metro area
https://factfinder.census.gov/bkmk/t...60%7C070%7C071
Durham–Chapel Hill metro area
https://factfinder.census.gov/bkmk/t...60%7C070%7C071
The Census Bureau's user interface is quite poorly designed. You have to select data from many different tables. You can't just tell them which data you want and let them get it from whichever table has those data. So you end up doing a lot of trial and error just to find the right tables. You have to guess the content of each table from its title.
Then there are many strange behaviors in their website. For example, if you visit one of links I have given you above, and if you bookmark the page that you reach using your web browser's bookmark mechanism, that bookmark will not send you back to the same page. Instead you have to click on a bookmark button on the page and explicitly copy-and-paste that. A properly designed website doesn't make you go to this much effort just to bookmark a page.
If you have too much data in the final result, then you can see the result once; but the resulting bookmark (even if you use their provided bookmark button) won't load the next time you visit it, as their website exceeds some internal limits and gives you an error message. With some trial and effort, I was able to get data using only a subset of attributes to avoid running out of memory. Combinations of more than two ethnicities are missing from the above bookmarked pages for this reason. If somebody identified themselves as belong to three ethnic groups, they will not show up.
Due to the many issues I encountered, I am not sure if the bookmarks I have given above will work for everybody. Try with Google Chrome on a desktop if you have problems in any other environment.