What does colour have to do with it?
If you are talking about an elderly person who fell over then that is relevant information. The fact that they are elderly and fell over means that, perhaps, they could have been hurt more than a younger person - when we hear about elderly people falling, we hear about broken hips etc, in a way that we just don't about younger people. So, depending on the circumstances, it may have been relevant to mention that the person who fell was elderly.
However, there is no relevant reason to mention the colour of someone who fell. A person's colour, unlike age, does not have the potential to make a fall more serious, or mean they need more help to get up, for example.
It isn't about mentioning or not mentioning age, colour, disability... it's really simple - is the insertion of that information relevant or even could someone reasonably think it was relevant.
I was talking to a woman on the bus, she was saying isn't it weird that we've had so much snow recently! - fine. Reasonable.
I was talking to a black woman on the bus, she was saying isn't it weird that we've had so much snow recently! - insertion of colour totally irrelevant and therefore meaningless.
I was talking to a black woman on the bus, she was saying isn't it weird that we've had so much snow recently and she was saying she's from Kenya and when she first came here, she couldn't believe how cold it could get. - I would argue that the colour of her skin is still unnecessary because it's her nationality that she is mentioning, but I can see how some people would think it was relevant.
and I know, I have used the word relevant so many times it's lost all meaning 
but that is the top and bottom of it. - What is the reason a description of the person has been included - is it integral to the story.
More often than not - it isn't.
And more importantly, you never get I was talking to a white woman, I was talking to an able bodied man...