This reminds me of the episode of South Park with the N-word. We just don't get it. I agree with others in this thread that painting one's face black as part of a costume isn't inherently racist, but I'm coming at it from the perspective of a white person who has literally never had to deal with racism. That's not the same perspective classy has. I don't get it, but that doesn't make his point of view wrong, nor does it mean he has to justify his feelings on the matter to us. We're not coming from the same background; we just won't get it.
That said, if I saw someone white wearing the Urkel costume, I would not jump to "Urkel," I would just assume they were going as a generic awkward dork. Using blackface would immediately solidify it for me, although it might also make me slightly uncomfortable depending on how they did the black makeup. Similarly, if I saw a black person dressed in Lincoln attire, I would jump to "black Lincoln" rather than just Lincoln. When you're dealing with historical characters that we know the race of, it's hard not to think about the difference in skin color. Maybe that's subtle racism, I don't know. That's just my own experience.