I regret that I am not clear as to what you intend by‘arisch’. I am not of Aryan extraction: that is Indo-Iranian; as far as I am aware none of my ancestors spoke Hindustani, Persian, Gypsy, or any related dialects. … But if I am to understand that you are enquiring whether I am of Jewish origin, I can only reply that I regret that I appear to have no ancestors of that gifted people. … I have been accustomed, nonetheless, to regard my German name with pride, and continued to do so throughout the period of the late regrettable war, in which I served in the English army. I cannot, however, forbear to comment that if impertinent and irrelevant inquiries of this sort are to become the rule in matters of literature, then the time is not far distant when a German name will no longer be a source of pride. — Draft letter answering questions about his ancestry made by his German publishers.

My Take – Sometimes, a well worded “Go screw yourself” is all you need.  Tolkien was being asked how true to the Aryan ideal he was, and if he was at all Jewish.  He replied that he was neither, but the fact that he was even asked made him regret being German.  Purity tests only show the insecurities and stupidity of those administering them, especially when it comes to something those being tested are born with.