Well, firstly, the professor is very wrong to call that 'blackface.' Typical blackface was done to play the part of a Black person, usually a slave. While some forms of blackface had the non-vindictive intent for White people to perform ethno-African music and dance (what we would call cultural appropriation), way too often it was to mock those of African descent.
So in Mary Poppins, neither Mary not the chimney sweeps are in any way acting like any ethnicity of color. They retain their usual accents and dance in typical 'White' dance hall fashion while singing a middle of the road Broadway-esque tune. That ain't blackface.
However... the professor points out that in Travers' books, she had ordinary White British folk make insulting remarks about chimney sweeps. And how did they disparage them? By likening them to people of African descent. That's racist. Period. There's nothing wrong about being from African descent or having dark skin. The professor points out that later editions of her books removed those racist remarks.
Now, getting back to Mary Poppins. We find that we do indeed have a White British person make an insulting remark about the chimney sweeps. The Admiral calls them "Hottentots." While technically a correct term for certain South African peoples in the mid-20th century (now deprecated, use the actual tribal name); it was widely used, however, pejoratively. In fact, he regarded Hottentots as a people that one should open fire on. So, yeah, he wanted to kill what he thought were Africans because they were Africans because he thought the chimney sweeps' skin was black. That's racist.
Now, to the movie's credit, the Admiral is depicted as batty and perhaps a bit senile. And the movie goes out of its way to portray sweeps as lucky and jolly. Although... that starts to get a bit close to the racist tropes of "the happy negro" or "the magical negro" (cf. Song of the South), but applied to sweeps. So, don't feel bad about the sweeps' horrible working conditions and their black lungs... they're magically jolly!!