It is up to primary schools to choose what they teach about same-sex relationships, the education secretary has said.
Damian Hinds has written to head teachers saying they are encouraged to teach children about LGBT issues if they “consider it age appropriate”.
He said heads should consult parents but reassured them parents had no right to veto what was taught.
It follows protests over the content of lessons in some schools in Birmingham.
Rallies have been held outside the city’s Parkfield Community School in protest at the “No Outsiders” programme, which teaches pupils about diversity, including LGBT rights and issues of race and religion.
Some parents said they believed the lessons “undermined parental rights and authority” – despite Ofsted’s view that the lessons at Parkfield were age-appropriate..
Parkfield assistant head Andrew Moffat, who created the No Outsiders programme, told Sky News he has received a death threat, while others involved in the row have also reported feeling “alone” and unsupported.
The school and four others in Birmingham have now suspended teaching the No Outsiders programme.
The controversy has spread further afield, with parents in Greater Manchester saying they will remove their children from sex and relationship lessons.
In his letter to the National Association of Head Teachers (NAHT), Mr Hinds says reports of teachers feeling intimidated are “concerning”.
He suggests listening to and understanding the views of parents as a way schools can “increase confidence in the curriculum”.
But he writes: “What is taught, and how, is ultimately a decision for the school.”
And he adds: “I want to reassure you and the members you represent that consultation does not provide a parental veto on curriculum content. We want schools to consult parents, listen to their views, and make reasonable decisions about how to proceed… and we will support them in this.”
In response, the NAHT said its members were “encouraged” by the letter and called for parents’ protests to stop.
Paul Whiteman, general secretary of the union, said: “This letter confirms that whilst school leaders are required to involve parents and the wider community in the planned content of the curriculum, consultation does not provide parents or others with a veto on curriculum content.
“Schools that take this approach will receive the full support of the government.”
He added: “There is clearly more to be done in Birmingham and in other areas where protests and disagreements have happened.”
Relationships education will be compulsory for all primary pupils from September 2020. Sex education will also be compulsory for all secondary pupils from that date.