Well, I think it depends on what you did as a "youthful act".and what you've done since.
I agree that people can and do change, but mostly they don't. AND the older you are, the less likely you are to change.
"I've changed" said every prisoner ever before his or her parole board, but mostly they haven't. Again, some do change but not all or even most.
Personally, I think he should resign. This incident didn't happen when he was 16 (as posted above, this is a great age to do stupid stuff). He was in medical school. That means he was between 22 and 26 (or older). Old enough that he is considered an adult by any measure. He can treat patients in hospitals at this point and he should know better at this point. So the question becomes, has he changed? And IMHO, you'd need to show me something that indicates you have changed rather than a lack of evidence that you are racists.