Sure Austin is a little blue bubble in Texas. However, most laws that impact employers are made at the state level, and Texas is a much friendlier climate and has less regulation. This does change the situation for residents of “blue” cities like Austin.
Tons of people are moving to Arizona and Texas from the Midwest and California. Now these states are turning blue, but the policies that made them attractive to those people (less regulation, resulting in more housing built and more jobs) are definitely not “democrat” policies.
No one is leaving Democratic states to go to some hell-hole Republican area. They are leaving Democrat cities to live in OTHER Democrat cities, the only difference between cost of living. That's it, simple as that. It has nothing to do with "wokeness" etc. It's basically, Austin cheap, San Fran expensive.