As of May 21, no Texas Government entity at the State, County, or Local/City Level may issue a mask mandate or requirement. Violating entities are subject to a $1,000 fine per occurrence. As of June 4th, no Public School may require masks for students, teachers, staff, or visitors.
Source: GA-36 EO from Texas Website
Archive -> https://archive.is/3oyR6
Vaccine Passports were addressed in GA-35 EO issued last month. It is our hope that it will get codified as legislation in an Emergency Session.
https://gov.texas.gov/uploads/files/press/EO-GA-35_private_health_information_protection_vaccines.pdf