The majority of people approve of schoolchildren being educated about gay relationships, despite some public protests, according to a survey.
Most also support transgender people being able to self-identify their sex, the research published on Thursday suggests.
New guidance on relationships and sex education, which will be compulsory from 2020, and require pupils to learn about LGBT families, was published last week by the Department for Education.
There have been demonstrations by some parents against schools teaching about LGBT relationships.
But the poll, conducted by YouGov for PinkNews, showed that 59% of people backed LGBT relationship education in schools, while 25% said children should not learn about gay relationships in schools, and 16% were unsure.
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.
She said such education is not “propagandising” or about “trying to turn people gay”, but instead is 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% gave their backing, while 23% said were in opposition and 21% 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 that the process of acquiring a Gender Recognition Certificate will be easier, cheaper and less intrusive.
The outgoing Prime Minister said on Tuesday that the work was “vital”, as she re-stated her backing for the 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 ground-breaking 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.