May I weigh in? I think, maybe as a German born in the 1980s, I may understand a bit of the guilt over one's ancestors' sins.
To this day, Germany pays reparations to the survivors of the Holocaust and the decendents of those who died. Is this right? Absolutely, because the German nation did horrible wrongs, and these reparations are the least we can do as a nation. Note, those reparations I speak of are paid to individuals, not nations. And even though I myself, as someone born almost 40 years after the end of the Third Reich, am not responsible for those crimes, I sincerely believe that the people of Germany have to pay those reparations.
Now, in the case here, it might not have been exactly the same, but there are enough similarities. The nation did wrong, the society did wrong, and a particular group of people suffered heavily. I think we all know racism didn't end with slavery, and it showed that it was not enough just to end slavery. Even not being slaves anymore, black people still did not have the same rights, and it was not that long ago that they did. Some of those rights they only got by law, meaning on paper, but the institutions of society, be it educational, judicial or economic institutions, still could and can get around those laws. Black people still are heavily at a disadvantage, even if some individuals among them may not feel that way.
And it is the duty of society, and thus of the state as the democratic representative of society, to make up for it. And while you personally may not have been responsible for societies past wrongs, as part of that society, you must share that duty.
Of course, it goes without saying, other specific groups of people have been openly discriminated against by the state and private institutions, and society must also strive towards righting those wrongs as well.