It wasn't really about separating Jewish blood from Aryan blood. That was just the Nazi propaganda as propaganda has to be designed with the lowest common denominator in mind.
It was about removing from society people who considered themselves Jews. In the past, as during the Spanish Inquisition, the Jews were removed from society according to religion. So a Jew sould avoid deportation simply by getting a baptism and "converting". Obviously the Spanish were faced with the problem of the large numbers of Jews who converted insincerely in order to escape deportation and secretly continued to practice judaism. This led to the Spanish Inquisition investigating people suspected of secretly practicing judaism.
The Nazis were aware of the Spanish experience and they decided therefore to base their deportations on blood so as to avoid the problem the Spanish had where Jews converted insincerely. By doing it by blood they avoided the problem of insincere conversions.
All the talk about racial purity when it came to Jews vs. Aryans was merely propaganda. The proof of this is how Hitler himself declared Jews to be Aryan. When questioned about the Milch matter Goering said something like "I decide who is Aryan and who is not". If Hitler himself declared Jews to be "Aryan" then we can see that the talk of racial purity as it related to Jews vs. Aryans was just propaganda.
As it says in this website http://www.kansaspress.ku.edu/righitpix.html:
""Half-Jew" and later Luftwaffe General Helmut Wilberg; Hitler declared him Aryan in 1935."
So Hitler himself declared Jews to be "Aryan" by fiat.