Usually people use “may” incorrectly by using it as a substitute for “might.” (Old joke warning:) An example of using “can” incorrectly as a substitute for “may.”
- “May” refers to permission.
- “Can” refers to ability.
- (“Might” refers to possibility.)
A long time ago I worked on a math textbook project. I got kudos for the word problems I wrote, but the mathematicians insisted that we use “can” when “may” was correct, so maybe the language is changing.