LONDON — In new rules to counter bullying in its 4,700 schools, the Church of England said on Monday that children should be able to “play with the many cloaks of identity” in the classroom, fueling a debate over the handling of gender among the very young.

The discussion has illuminated deep divisions between Anglican conservatives defending traditional values and those seeking a more liberal approach.

In a directive called “Valuing All God’s Children,” the church said elementary school students “should be at liberty to explore the possibilities of who they might be without judgment or derision.”

“For example, a child may choose the tutu, princess’s tiara and heels and/or the fireman’s helmet, tool belt and superhero cloak without expectation or comment,” it said. “Childhood has a sacred place for creative self-imagining.”