First of all there is no racism in Islam. I will try to explain as much as I can. According to the fatwa of The General Presidency of Scientific Research and Exile (Saudi Arabia), if Zakah money is given to anyone other than the members of the Prophet's (Sallallahu'alayhiwassalam) family and they then give it as a gift to any member of the Prophet's (Sallallahu'alayhiwassalam) family, it is permissible for members of his (Sallallahu'alayhiwasssalam) family to take it and benefit from it.
They cited the following hadith to prove it:-
The Messenger of Allah (peace be upon him) sent me some lamb from the
Zakah. I sent
Aishah some of it. When the Messenger of Allah (peace be upon him) came to Aishah, he asked, "Do you have anything (to
eat)?" She said, "Nothing, except the lamb that Nusaybah (Umm
`Atiyyah's nickname) sent us from that which you gave to her. He said,
"It has reached its proper place. (Muslim and Bukhari)
Here is the another Hadith:-
It was narrated from Anas that some meat was brought to the Messenger
of Allah and he said:
"What is this?" It was said: "It was given in charity to Barirah." He
said: "It is charity for her and a gift for us." (Sunan an-Nasa'i
Secondly, as far as the phrase "Zakat is part of people's impurity" is concerend, it does not mean that "people" who receive Zakat are impure.
In the Hadith scriptures, it has been narrated,
"The Muslim is not made impure." (Recorded by Nasa'i, Vol. 1, Book 1,
"A believer never becomes impure" (Sahih al-Bukhari 285)
Secondly, as far as the word "people's impurity" is concerned, it does not literally mean that people are impure or the people who receive Zakat are impure rather it is referring to the impurity of wealth in posession of people.
As the hadith scriptures say,
Allah made Zakat a purifier of the property." (Sahih al-Bukhari 1404)
I hope it answers your question.
Allah Knows Best.