Most of the public approve of schoolchildren being educated about gay relationships, despite some protests, according to a survey published today.
The majority of people also support transgender people being able to self-identify their gender, the research suggests.
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Compulsory LGBT-inclusive relationship education for primary-age pupils was introduced last week.
Some parents have demonstrated against the move.
But the poll, conducted by YouGov for PinkNews, showed that 59 per cent of people backed LGBT relationship education in schools, while 25 per cent said children should not learn about gay relationships in schools and 16 per cent were unsure.
The guidance states that pupils must understand and respect that some people are LGBT and that the law "affords them and their relationships recognition and protections".
Parents at two schools in Birmingham have protested over the classes, with Anderton Park Primary School requiring a court injunction to ban demonstrations around the site.
Labour's Angela Eagle, who became the first openly gay female MP when she came out in 1997, was praised for her impassioned defence of LGBT equality teaching last week.
Ms Eagle said LGBT relationship education is not "propagandising" or about "trying to turn people gay", but about respecting the right to have an "equal welcome in school" and not be bullied.
The survey of 1,720 adults, carried out last month, also found that the majority supported individuals being able to self-identify their gender as one other than that in which they were born.
Some 56 per cent gave their backing, while 23 per cent said they were in opposition and 21 per cent were undecided.
Theresa May last year ordered a consultation on the Gender Recognition Act, which allows people to change their legal gender.
It is hoped this will make the process of acquiring a Gender Recognition Certificate easier, cheaper and less intrusive.
The outgoing prime minister said on Tuesday that the work was "vital", as she restated her backing for LGBT relationship education.
"I know that policy in particular has been controversial in some areas, but teaching all children about respect for difference is a core British value, something I and every government should always stand for," she said.
PinkNews chief executive Benjamin Cohen celebrated the poll's findings.
"More than two years since the prime minister made a groundbreaking pledge in favour of trans equality, it is clear that the public backs reforming the law to allow trans people to self-identify in order to receive a Gender Recognition Certificate," he said.