Abbott: Texas schools cannot force students, staff to wear masks after June 4 Published County officials have mixed reactions to Abbot's mask mandate decision One of governor Abbott’s biggest in-state rivals is Dallas County Judge Clay Jenkins, who has rarely agreed with any decision the governor has made during the pandemic. It's a different story in neighboring Tarrant County. DALLAS - Gov. Greg Abbott has issued a new executive order that will soon force Texas school districts to drop their mask requirements in the classroom. The new order, which goes into effect on May 21, imposes a fine of up to $1,000 on any city, county, school district or other governmental entity still mandating masks.