At about the same time as the concept of "race" (and with it, "nationality") itself came into existence - that is, in such complex and varied ways across time and space that you can't pinpoint any year, or even century, between 380 A.D. and 1933 that the transition occurred. Yes, the proto-racialist limpieza de sangre in Spain had a huge impact on Jews living there, but it's not like all of Europe suddenly came to appreciate this new definition of humanity that the Spanish crown invented. And even limpieza de sangre was only proto-racialist; it was a discriminatory policy directed against two specific minorities, not a universal system of classification like the 19th- and 20th-century racialists (or, for that matter, 21st-century censuses) drew up. I don't really buy the argument that limpieza de sangre was an ideology, in the way we'd understand it today, or even a particularly clear precursor to it.
Actually, I'd say that the idea that Judaism is "just a religion" is about as new as the idea that it's a race. Medieval economics, especially the relationship between the town and countryside, encouraged the segregation of Jews as an urban caste; that system started to break down in the Early Modern era, which brought back serious ideas of mass conversion, as opposed to occasional pogroms or explusions. Consider the case of Martin Luther: in the earliest years of the Reformation, he naïvely thought that Jews would convert to the purified Christianity he'd set about making, and so had (for his time) relatively liberal attitudes toward them. At that time, he condemned discrimination against them as an impediment to their conversion. When they failed to convert - no surprise - he turned into the vicious anti-Semite of On the Jews and their Lies. But he never gave up on the idea of conversion, leading to this bizarre paragraph:
Well, it seems bizarre to us today, but it makes sense if you consider Luther's entire worldview as a spiritual revolutionary. The idea that "Jews are Jews, nothing to be done about it" can be interpreted either as racialism, or as part of the medieval *caste system; but you can only conflate the two with regard to a third alternative, that every human being has an equivalent individual soul regardless of ethnicity and economic role. That's an invention of early modernity - expressed in Germany as Protestantism, but filtering gradually through all of Europe - just as much as racialism is. It's even more interesting, and more historically accurate, to see racialism and humanism as the two sides of the modern coin, but that's a lot to discuss.