My understanding is that Austin is actually politically moderate, though the strong authoritarianism is much more troubling to me than the heavy political slant.
The main issue is that Austin, like all other municipalities in Texas, is governed by the Legislature of the State of Texas. Home rule cities in Texas have legislatively-granted broad authority but the Texas constitution doesn't protect the actions of home rule cities very much. The legislature of Texas has routinely been very fast to pass laws pre-empting city ordinances they don't like. This is in comparison to the constitutions (and constitutional traditions) of some other states where the legislature is largely expected to let local government do its thing while the legislature concerns itself with the state as a whole.
Or, put another way, Austin might be the deepest blue on the entire continent but that means little when the state government is in direct opposition, and has been for decades.
That is my understanding as well. Austin itself feels like a city plucked out of blue state, but I didn't want to risk being caught in the growing Texan zeal with nowhere to go.
Latitude doesn't help so much, you need altitude, or oceanfront and hope the currents dont shift and you are above the new high water mark. And when the refugees arrive your deed won't count for much, but at least you won't be a refugee.
I just moved back to the US after roughly 10 years in Hong Kong. If they pay you enough to move in and move out, don't worry about it (unless your kids are in school).
Or, put another way, Austin might be the deepest blue on the entire continent but that means little when the state government is in direct opposition, and has been for decades.