> A quick look at Redfin says tax on this $385k home is about $564/mo
The tax estimate is based on an assessment based on a sale that happened 6 years ago, which ends up valuing the house at $100k (roughly 25%) less. :-) A new buyer would have a hard time paying the same tax because this would involve successfully arguing that the property is worth $100k less than what they just paid for it. $800/mo is likely in the ballpark of what the new owner would be looking at.
EDIT: Since millage rates are public, we don't have to guess. The topline Austin (Travis County) millage rage is 2.1767, so if that property were in the city of Austin its taxes on a $385k assessed value would be 8,380.29, or $698/mo. It may actually be in Pflugerville (hard to tell at a glance) where the taxes are lower due to letting Austin taxpayers pay for the big shared muni services.
The other effects are interesting, but my experience living in TX is it is definitely not a low-tax state.