This seems to just be some unweighted survey, not sure why 538 added this. The party registration of the sample is very out of line of the actual statewide party registration composition (way too Dem) and it's also way too old.
Kentucky actually has one of the highest percentages of registered Democratic voters in the country. LOTS of DINOs and ancestral Dems. I’m not sure of the exact numbers nowadays, but they did specifically ask about what party you are REGISTERED as, not identify as, so it might not be as big a deal as you think.
I know this and I specifically said party registration in my post. The party registration breakdown of registered voters is 47% Dem, 44% GOP, 9% other, which is way off from this poll which has 56% Dem, 37% GOP, 7% other. In 2016 among people who actually voted the breakdown was 51% Dem, 43% GOP, 6% other, while the overall voter registration partisan breakdown was 51% Dem, 40% GOP, 8% other (a good number ancestral Dems have changed their party registration since 2016). The current breakdown of people who have already voted in Kentucky this election is 51% Dem, 43% GOP, 6% other, and is bound to become more GOP with the remaining days of early in-person + election day voting. So overall I think it's reasonable to think that a 56/37/7 sample by party registration in Kentucky is far too Democratic skewed.