Parents would have the ability to exclude their children from some elements, including the most explicitly sexual, but not others, and not after age 14, said Mr. Hinds, a member of the Conservative government. From age 15, it will up to the student to decide whether to participate fully.

The curriculum developed by Britain’s central government will be mandatory for any school in England that receives government funds, including religious schools; it was drafted under a 2017 law instructing the government to update the policy. Scotland, Wales and Northern Ireland have separate standards.

An online petition asking for parents to be given broader power to opt out had gathered more than 100,000 signatures by Monday morning, prompting Parliament to debate the matter — an airing of views that did not affect the policy — while dozens of protesters gathered outside.

The government was “pretty much indoctrinating the children with a specific ideology that there is no such thing as right or wrong, it’s just whatever you like basically,” said Musa Mohammed, a 32-year-old father of three who joined the protest. “These are our children — they belong to the parents, they don’t belong to the state.”

Britta Riby-Smith, a mother of three, said she was there to support “the Christian cause.”

Under the new curriculum, as the children get older, “the L.G.B.T. kind of agenda becomes stronger,” she said. “This is something I want my children to know about — I don’t want them to be ignorant, definitely not — but I would like to teach them about this myself.”