Can you not understand? The practice of "blacking up" has seriously unpleasant associations for black people - of segregation, discrimination, disrespect, ridicule, denigration, etc, etc. Can you not put yourself in someone else's shoes and see how it feels for them or at least understand and accept that it hurts and offends many people?
I think the phrase "political correctness" is a a misleading one, which evokes a knee-jerk reaction. It is not about politics (or only politics in its widest sense - not party politics). It is about having an awareness of people's feelings and treating everyone with courtesy, respect and decency.
It has been acknowledged that many people who watched the Black and White Minstrel Show (that included me, as a child, and my parents) were sadly ignorant of the offence it caused in portraying and reinforcing in the public psyche a gross caricature of black people. But that was at least 50 years ago, not 20.
As Trudeau himself said, he should have known better. When he came to office I was hoping he would be different but this latest revelation, on top of the previous corruption scandal, has changed my opinion of him.