Governor Abbott's Executive Order No. GA-34 says that businesses and other establishments may require employees or customers to wear masks. It also allows law enforcement to enforce trespassing laws and remove individuals who refuse to wear a mask at a business that requires them.
According to the Equal Employment Opportunities Commission (see FAQ G.2) an employer can require employees to wear protective gear (such as face coverings or gloves). Employees may make a request for a reasonable accommodation under the ADA or a religious accommodation under Title VII of the Civil Rights Act (such as a modified mask that can be worn with a religious head covering). Employers should provide the modification or an alternative modification unless it would create an “undue hardship” for the employer.