I was thinking a little bit about the outrage the blackface induces among the masses. It goes by the logic that black people were oppressed and were not given many opportunities purely because of racism.

I'm sure you didn't mean this, but saying black people "were oppressed and were not given many opportunities" comes off as whitewashing and minimizing what black people historically experienced. Chattel slavery in the Americas, sex slavery of captured black women and routine castration of captured black men during more than a thousand years in Arab and Ottoman slave trades, lynching, Jim Crow, apartheid, the sorts of horrors King Leopold of Belgium and other Europeans inflicted on the people of Africa, mass incarcerations... and so on are a bit more serious than the wording you've used suggests.

Black feminists I know have said they find comparisons between blackface and both drag and transing ("womanface") to be offensive and hurtful to black people, and they've explained why. Therefore, my own preference is to criticize drag and drag shows on their own, without likening them to blackface and minstrel shows.