The more generalized version of "republican" is hardly in common use any longer, and certainly in far less common use than the reference to the political party; the latter is, for the most part, what a significant portion of the audience will first think of when they see "republican." That they could think of something else, or would think of something else were they to see the word in the right context is not besides the point or a counter-argument to it, but rather is the point; the exact same is true for a different understanding of race. Even if the finer points of the renaissance usage and its origins aren't common knowledge (any more than the average person could explain the nuances or discursive origins of republicanism) I would argue that the usage itself is generally familiar to anyone acquainted with history, historical fiction, vernacular pre-modern fiction and drama, or (most relevantly) fantasy media of all kinds. In other words, our first reaction might be to think of something else when someone says race, in general, but the first thought when someone refers to a race in fantasy media (or a philosopher refers to "the race of men," or a ballad calls Clan Donald a noble and courageous race), specifically, will be of something much closer to the renaissance usage than the contemporary use.

This comment "if" not me arguing that we should assume they are using a certain form of the word because "why not," but that we should assume they are using the archaic form because that form broadly matches their use of the term, because that form arose from a worldview and system of knowledge in our world roughly analogous to the system of knowledge of the setting's world, and because the modern use of the term neither matches the use we see nor matches the implicit discourse or system-of-knowledge seen in the setting. I am acknowledging the existence of history and context, you are obliterating them to try and support your reading with an appeal to its socio-political relevance. It is relevant to your overarching point, because a significant portion of your defense of your point relies upon the Elder Scrolls idea of race mapping to the modern idea of race well enough for you to accuse detractors of racism.