Local mask mandates pop up in defiance of Gov. Greg Abbottâs executive order banning COVID-19 restrictions Houston Mayor Sylvester Turner is the most recent official to defy the governorâs order. He announced Monday that the cityâs nearly 22,000 city employees will be required to mask up inside city buildings where social distancing is not doable LM Otero/AP FILE - In this Wednesday, March 17, 2021, file photo, Texas Gov Greg Abbott speaks during a news conference about migrant children detentions, in Dallas. (AP Photo/LM Otero, File) By: Colleen DeGuzman and last updated 2021-08-04 16:36:54-04 Local mask mandates are popping back up across Texas â even as Gov. Greg Abbott has stressed that local officials who try to enforce restrictions aimed at reducing spread of COVID-19 will be penalized.