UpdatedWed, May 19, 2021 at 9:56 am CT Reply The Magnolia, Montgomery and Conroe school districts already set end dates for their mask policies. Gov. Greg Abbott signed an executive order Tuesday that prevents public schools from requiring masks after June 4. (Shutterstock) MONTGOMERY COUNTY, TX — Several Montgomery County school districts already are in line with Texas Gov. Greg Abbott's latest executive order concerning COVID-19 and mask mandates. Abbott signed an executive order Tuesday banning government entities from requiring masks. The order included public schools, which won't be allowed to mandate mask use on their campuses after June 4. New Caney ISD announced at its Board of Trustees meeting Monday that masks will no longer be required beginning June 1.