Being told to ‘check your privilege’ is not about anyone wanting you to:
Apologize for being yourself.
Believe that being yourself is bad or wrong.
Be ashamed of being yourself.
Feel guilty for being yourself.
What people mean when they say 'check your privilege' is:
You are inserting yourself into a conversation where you shouldn’t be.
You are making other people's pain all about your own feelings.
You are belittling someone else’s pain.
You are making some else’s fears/concerns/pain less important than your own sense of being comfortable (or uncomfortable) in talking about an experience.
In a nutshell, you are being asked to acknowledge what you are doing, apologize, and stop the behavior.