The article doesn’t say that people are leaving in droves because it’s a sanctuary city (though one person interviewed mentioned that). It says the top reason is the high cost of housing.
It doesn’t make sense for someone opposed to living in a sanctuary city to want to move to Austin as a remedy. Austin challenged Texas’ anti sanctuary city law in court.
https://www.usatoday.com/story/news/politics/2017/06/02/texas-sanctuary-city-lawsuit/366448001/