People often say after offensive jokes about said faith that it was racist. When did it become that a religion was a race?
Looking back on my knowledge, it seems like it might've started with Hitler, and his while "if your relative is a jew, so are you" policy, but it feels like it would have to have older roots than that for it to be as culturally defined as it is.
Jews had been called "race" and "nation" long before Hitler, in tsarist Russia. The earliest mentions of the expression "Jewish race" (yevreyskaya rasa) in corpus of Russian texts can be found in P. I. Kovalevskiy's 1910 text (3 examples) and in Zhabotinskiy's 1911 text (4 examples).
Also, in tsarist Russia, Jews were called "nation" (natsiya), despite they didn't have their own state at the moment. The earliest mentions of expression "Jewish nation" (yevreyskaya natsiya) come from 1869,1872, and 1903. For example:
[1] - 1869, I. A. Goncharov:
Such intellect, by the way, was enveloped in long opression by exhausted and scattered Jewish nation (yevreyskaya natsiya), while secretly making thair way through the people croud, saving their lives, property and right for existing by ther smartness.
[2] - 1872, M. Ye. Saltykov-Schedrin:
entered the nicest an the most honest Jew, named Goldenschwein, who, as I learned later, was kept in psychiatric clinic too and was obsessed with the idea of renessance of Jewish nation (yevreyskoy natsii).
[3] - 1903, A. V. Amfiteatrov:
"You, Ida, are Jewish, your Jewish nation (yevreyskaya natsiya) are practical, therefore, you will manage the business - take the keys and command!"