When you think you've overcome dualistic thinking, you probably haven't.
When you get to the place where there is no good and evil, no self and other, and when you are able see these things as judgments and illusions — you will very like reject the old reality you used to live in where these things actually existed. In your new reality, none of these things are real, there are no opposites, nothing is separate, and all things come and return to the same source and are part of one unified whole. Hurray! You have overcome dualistic thinking.
However, to the extent you are now firmly rooted in this non-dualistic experience of reality, you have actually engaged in a different type of dualistic thinking. Just as you used to believe something is either good or evil, self or other, it can't be neither or both at the same time; now, in your apparently "enlightened" non-dual state of observation, you are, in fact, on one side of a new and more subtle "either/or" proposition — reality is either dualistic or non-dualistic, it can't be neither or both at the same time.