In the case of the piano school, my wife believes that they tend to have favorites, and once that opinion is formed it is easy to find additional evidence to reinforce that thought. Whether intentional or not, it is probably true. I do not care, but she does.
So yes, you can treat difference customers differently, even charge some more and some less. But be aware that people do not all think the same, and a slight difference in treatment could result in a lot of bad buzz.