AP Style holds that the proper names of nationalities, peoples, races, tribes, etc., should be capitalized. Some common examples,
- Arab, Arabic
- Chinese (both singular and plural)
- Eskimo (plural Eskimos)
- French Canadian
- Japanese (singular and plural)
- Jew, Jewish
See the page on AP Style Race for guidelines on when racial identification is pertinent to a story.
You should only use derogatory terms in direct quotes when they are essential to the story and should then be flagged in an editor’s note below.