Many grocery stores "complied" by replacing the single-use bags with much thicker "reusable" plastic bags. So now customers still don't bring their own bags into the store, the new bags still aren't easily recyclable and I suspect most are thrown away just as before.
Edit: on the other hand, the city of Austin's waste management is very supportive of recycling and hopefully they'll support plastic film in the single-stream collection and make it much easier for the average person to do the right thing.