More Texas public-school districts have adopted rules allowing employees to carry guns on campus in an effort to deter—or quickly respond to—shootings. Still, most schools have chosen not to arm their staff.

Texas is among at least eight states that have passed laws since the 2012 mass shooting at Sandy Hook Elementary School in Newtown, Conn., allowing school employees to carry guns on campus, the National Conference of State Legislatures said. At least 78 of Texas' 1,024 districts have reported adopting a "school guardian"...