It looks like the core of downtown Austin has doubled in population between 2010 and 2020, going from 5000ish people to 10000ish people. If it's anything like the downtowns of other big Southern cities, it probably didn't have too many people before the present-day boom and a good chunk of those new residents are condo-dwellers paying a premium to live downtown.
Austin has a lot of interesting and culturally rich neighborhoods, so choosing to live downtown means you're probably more focused on work instead of experiencing the city's culture. People of that class and with those priorities voting to the right of the rest of the city makes sense imo.
Interesting point, but counterpoint: the downtown is a neighborhood in itself and generally those who are willing to give up a single family home with backyard for living in a dense walkable urban neighborhood skew heavily D.
There are a lot of people who prioritize walkability and density, but very few where that's the only factor. People who prioritize those factors are generally also going to be interested in culture, the arts, etc. and I suspect other areas of the city are going to be a better fit for that, especially when they're probably much cheaper too. Austin isn't the sort of place where you can easily get away with living without a car anyway; the people in downtown probably have parking garages in their buildings.
It's an imperfect analogy, but to use a New York parallel it's the same reason why people in Midtown or the Financial District are to the right of hipsters in gentrifying Brooklyn, except some of them vote Republican because Texas.
I should also caveat this with the fact that I don't know much about the built environment in Austin and am somewhat extrapolating based on places I know better -- so this could easily be wrong.
