I think that your question is asserting that the ruling in Edmonson sets up a special privilege for African Americans. I have edited your question to show this.
I do not agree with this statement. The Edmonson ruling does not set up a special privilege for anyone and it does not apply solely to African Americans.
What the decision in this case said is that attorneys in a civil case may not use their peremptory challenges solely on the basis of race. In other words, attorneys may not throw people off of juries simply because they do not like the race of the potential juror. This decision does not say that only African Americans are protected from this practice. Instead, it says that no one may be excluded from a jury in a civil trial (there is the same rule in criminal trials that existed before Edmonson) simply because of their race.
This ruling also does not set up any quota with regard to juries. There is no need to make sure that you find some number of people of various races. Instead, it simply says that potential jurors cannot be excluded based on race.
Therefore, this ruling is neutral with regard to race and it is not right to say that it privileges African Americans.