While I can't really speak to the history of the concept of race in general, this did indeed mark the first time that Jews were singled out, in effect, as their own race, rather than just as a religion. (While there was certainly a similar dynamic with Muslims at the time, I'm less familiar with the nuances.)

Obviously there was no concept of genetics at the time; the idea, at its inception, was that Jewish converts to Christianity may revert, and therefore need to be viewed with caution. While not a brand new idea (it had been in place in Visigothic times in Spain as well), it was new for the time, as for several centuries, a Jew who converted to Christianity was considered as Christian as any other, and in fact Jewish apostates could ended up in powerful positions in religious orders due to their knowledge of Hebrew and Judaism and subsequent ability to fulfill important functions such as assisting in the conversion to Christianity of more Jews and the translation of Hebrew copies of Arabic texts into Latin.

However, after the mass (essentially forced) conversion of Jews to Christianity in Spain in 1391, public sentiment against these converts by the public, suspicion that they were not "true" Christians, grew so strong that a division between "Old Christians" and "New Christians" became clear and eventually enshrined into law in the statutes about limpieza de sangre. These converts were rising in society in ways that they couldn't have as practicing Jews, and they weren't necessarily keeping Christianity fully- after all, their conversions had been forced and often they didn't know much about Christianity to begin with, and wanted to cling to their original Judaism. Crypto-Judaism was a definite phenomenon at the time among the conversos, and while we can't know how many of the conversos participated, the phenomenon definitely tainted them as a whole in the eyes of the "Old Christians."

This was the backdrop against which the first limpieza de sangre statutes began to be enacted in the 1440s and 1450s. They never claimed a genetic difference- how could they?- but instead claimed an innate lower status for Christians who had converted from Judaism. This was far from uncontroversial- a papal bull in 1449 condemned these limpieza de sangre statutes, and generally they were as unpopular outside of Spain as they were within Spain. Even within Spain, they were also often unenforced. But the fact is that, for the first time, "blood" of those of Jewish origin was considered to be inherently different than "blood" of those of Christian origin. While for centuries Christians had maintained that the difference between Jews and Christians was that Jews clung to Synagoga rather than Ecclesia and stubbornly refused to embrace Jesus, now suddenly even that wouldn't erase the differences between the two- and not simply in terms of being suspicious of new converts for fear of reversion, as had occurred in Visigothic times, but even, in theory, in terms of deeming even the children and grandchildren of these converts as inherently different.

Even within Spain, limpieza de sangre statutes were never enacted on the national level, but rather on municipal levels and within private organizations, such as religious orders and universities. They really more than anything reflected the popular animus and resentment against conversos by Old Christians, which is seen even more clearly when one realizes how many of these statutes were enacted in the wake of anti-converso violence by Old Christians. Purity of "blood" in general was considered extremely important socially, and it was actually relatively easy to fake, being in many ways about appearances and proprieties.

While this can be seen as the root of racism against Jews- seeing them as inherently second-class rather than simply so due to their religion- at its core, limpieza de sangre still had religious roots, as it was about seeing these former Jews as inherently more heretical. There were none of the indications of antisemitic scientific racism which would come later about physical issues and stereotypes. But still, a conception of a separation between Christians of proven Christian origin and of proven Jewish origin to a multigenerational extent is significant in and of itself.