Then, based on what you said, science is often forced to cope with the supernatural: Logical self-consistency demands it.
Science can easily deal with the supernatural. People who believe in the supernatural are seldom pleased with the experimental results.
Looking back to the post you were responding to, I don't see the point you were trying to make.
The history of quantum theory and relativity are examples of instances where science had to deal with contradictory evidence. In such cases, what changes is our understanding of things.
Science deals with such changes in perception all the time.