You'd put quotation marks around a word or phrase when quoting someone;
... or when referring to a word as a word ("'Dog' has three letters") or naming something ("We named him 'Spot'");
...when referring to some types of thing by title ("Let's sing 'Clementine'");
...or you can also use it around words you consider dubious -- "scare quotes," they're called. But in your case: if they weren't treated equally in death, what is the purpose of the sentence? It seems to say that they were, but also that they weren't, and I don't know which you mean.
If it's the former, this works better:
This was the only moment blacks and whites were treated equally.
That is, in death, everything's the same. But if they weren't treated equally in death, tell us that:
This was the only moment blacks and whites might have been treated equally -- but they really weren't, because ...
Whichever one you mean.
Here's a legitimate use of scare quotes:
"Separate but equal" public schooling held sway until Brown v. the Board of Education.
This is scare quotes because you'd want to make it clear you don't think it was really separate but equal.
I personally think scare quotes should only be used if the quoted term was actually said by somebody somewhere, as it's illogical to use a dubious term if nobody agrees with it! But I don't know if you'd find that in a style book anywhere.
More on using quotation marks around words.