It looks like people turn up the twang when they want to be charming. I'm not aware of doing that consciously, but I'm aware of sounding more Texan when I'm talking to old people, Texans, political partisans (?), and strangers. I think thus fiddling with your own accent is less fraught in the United States than in, say, Britain. This story explains how researchers at UT's Texas English Project
studied baristas from Bouldin Creek by asking them to read "Arthur the Armadillo" out loud, twice: “To get a baseline of their maximum dialect speech, we asked them to sound really Texan,” Hinrichs said. “And we found all the textbook features of the Texas twang, like pronouncing words like ‘five’ as ‘faav’ and ‘pie’ as ‘pah.” Hinrichs said this finding confirms the Texas twang continues to exist as a resource, but people are using it more as a social commodity.