Absolutely. You know, I'm a relatively light-skinned African Canadian with a high level of education and a fairly high income. That would make my experience different from my father's in terms of experiences with the police. Although I would tick the box “black”, my father was much darker, had an accent and lived in very different circumstances than I do. That would be different again from a young indigenous female, who might be different from an elderly Asian female. I do an exercise in my inequality and criminal justice class on exactly that.
Intersectionality is important. None of us come into the world with just one identity. There are multiple aspects to our identity. When it comes to experiences of oppression, for many the axes of oppression are multiple and overlapping. Again, when we think about the fact that racism in our society increases problems of mental health, then we have the intersection of race and mental health that's very prevalent—for example, in the deaths of many African Americans in the Toronto area, they've been called, of course, because of mental illness.
So yes, it should be examined.