If people refuse to look at you in a new light and they can only see you for what you were, only see you for the mistakes you've made, if they don't realize that you are not your mistakes, then they have to go.

This quote is saying that if someone only sees you for your past mistakes, and won’t recognize that you have changed and grown since then, then it is best for them to leave your life. It is important that the people in your life are able to see you as a different, better person than the one who made the mistakes, otherwise they should not be a part of your life.