Why do modern Republicans reference the Democratic party's past conservatism as if it's a point for them?

The Democratic party used to be more ideologically conservative/Right-wing until the poles began to shift with FDR. Southern conservatives remained largely Democratic until the Republican party won them over in the 60s and 70s as the Democrats increasingly supported Civil Rights. By the time of Reagan, the Democratic party was associated with liberalism/progressivism and the Republican party with conservatism, as they are today. This was quite the opposite from the situation in the late 19th/early 20th century. Teddy Roosevelt (who founded the Progressive party) was a Republican who stood for larger government and liberal policies (as defined at the time)—an ideology that would now be associated with the Democrats.

Obviously that’s a condensed and simplified history, and I’m not implying that the early 20th century political climate was an exact mirror image of the current one, but my point is that I often come across Republicans online who note the early Democrats’ support for segregation and the KKK as signs that the Republican party is somehow morally superior, when all they’re doing is shooting themselves in the foot by condemning the stances of early conservatism/reactionism, thus implying that conservatives were on the wrong side of history then (and what does that say about modern conservatism?)

Yes, I realize this is more of a rant than a question, but I’m trying to spread the word about a really piss-poor argument (or have some light shed on it if there’s something I’m missing).

Disclaimer: I’m not a Democrat nor am I overtly liberal.