New draft guidelines on relationships and sex education (RSE) could create fresh problems for Charedi schools by recommending that LGBT issues should be "integral".
The proposals, released for consultation by the Department for Education this month, would apply to all schools, including faith and independent schools.
While new legislation gives religious schools licence to teach RSE according to their values, the consultation document suggests it will be hard to exclude certain topics.
The draft guidance states: "Schools are free to determine how they address LGBT-specific content, but the department recommends that is integral throughout the programmes of study."
Parents will retain the right to withdraw children from sex education, but not from relationships education. In theory, all of the parents of a school could state they do not want their children to receive sex education.
While relationships education is compulsory for primary schools, sex education is not.
The guidelines say secondary-school pupils should be aware "there are different types of committed. stable relationships" and how these might "contribute to human happiness".
Pupils should also be aware how stereotypes - particularly those based on sex, gender, race, religion, sexual orientation or disability - can cause damage.