A B&W Minstrel is a deliberate, offensive, derogatory portrayal of the black race.
To dress up as a minstrel is to impersonate something wholly offensive. The clothes, the facepaint are innocuous in and of themselves, but when used to represent an ugly and odious caricature, the meaning is plain.
Nazism is wholly repulsive to all people with any moral barometer. To dress up as a Nazi is to represent something repugnant and offensive.
Tiger Woods is a sportsperson of huge achievent. To dress up / make oneself up in positive tribute to him is not an offensive act.
What it is, as you point out, is a potent reminder to many people of a way in which something innocuous (facepaint in this instance) has been used to cause great offence, and do great harm. And the association for some people is strong enough to render any other meaning redundant. And this is reason enough to avoid imitation, however innocent.
However, there are many examples in the world of where something innocuous has yielded something both positive and negative. I remember the shock of seeing a Hindu swastika for the first time in India, and learning about its roots and how it became appropriated by the Nazis. My visceral reaction still overwhelms my logical thought when I see the image though, and I find it difficult to see it as anything other than negative. I accept that this is irrational, however. (as in, not a product of dispassionate reasoning, rather an example where my associations are so strong that I emotionally cannot override them.) However my logic compels me to accept the image is in fact, NOT offensive when used in its original form.
I think this is what I'm trying to say about the facepaint issue.