You're comparing different things there: Republican is both the noun and adjective form, while Democrat is only the noun form. "Clinton is a Democrat" and "Bush is a Republican", but "Obama was the 2000 Democratic candidate" vs. "Dole was the 1996 Republican candidate".

You could try to adjust for that by comparing Republican vs. the sum of Democratic+Democrat, but that also pulls in unrelated uses of both terms: "democratic reforms in $countryname" and "Irish republicans", especially since it isn't case-sensitive. Which then probably overcounts "democratic", because it's used in that non-US-party sense more than "republican" is.

In general this kind of thing makes it very tricky to conclude things from pure word or n-gram frequency counts, since without more semantic annotation there are a ton of confounding issues.

If you graph "republicans" and "democrats", the graphs are almost identical.