It seems this issue came to media attention with Parkfield primary school in Birmingham in March 2019. However, similar disputes in Birmingham schools do precede this kerfuffle.
The school's leadership had started a 'No Outsiders' class. The point of this class was to teach children to be tolerant of people from different races, genders, or sexualities. This initiative failed completely when Muslim parents removed 600 children from classes for a day. This comes after 400 predominantly Muslim parents signed a petition in January demanding the lessons be discontinued.
The school's regulator, Ofsted, then stated that Parkfield had an "outstanding" record of "tolerance, acceptance and mutual respect". Direct quotation from the 14th March article in The Guardian:
Andrew Moffat, who was awarded an MBE for his work in equality
education, said he was threatened and targeted via a leaflet campaign
after the school piloted the No Outsiders programme. Its ethos is to
promote LGBT equality and challenge homophobia in primary schools.
Moffat, who has been shortlisted for a world’s best teacher award,
resigned from another primary school in Birmingham, Chilwell Croft
academy, after a similar dispute. He is also the author of Challenging
Homophobia in Primary Schools, a teaching document.
At one of the Parkfield protests, parents held signs that read “say no
to promoting of homosexuality and LGBT ways of life to our children”,
“stop exploiting children’s innocence” and “education not
indoctrination”.
The evidence suggests that Parkfield attempted classes which challenged prejudices against race, gender, and the LGBT community. These classes were rejected by Muslim parents on the grounds that this was equivalent to teaching their children to be LGBT. The government's schools regulator however sided with the school's leadership and concluded the school had a good record of trying to deal with prejudice.
Parkfield's Head, Hazel Pulley, has said the following on the issue:
It's really upsetting for our staff, some of them are becoming ill,
some of them really don't want to come to school. Some say they've
been shaking. Losing weight, not wanting to eat food at all. And the
reason why is because they're met, especially the teachers of young
children, with parents accusing them of things that are just not
happening.
For example, the parents of young children are saying "But you're
teaching them certain sexual activity, which we don't agree with."
Well we don't, we certainly don't do that. Or we're using clay models
or something to show children something of a sexual nature, we most
certainly do not do that. There's a real concern about the myths that
are out there, that we might be using, in assembly, pictures of our
partners or conversations with children and those things are really
not happening.
...I think it's very clear, from school that we would never ever
discuss sexual activity with very young children.
We don't know whether this is evidence of a deliberate smear campaign by parents, or just a case of mass hysteria due to ignorance or prejudice. Given Ofsted approval, it seems unlikely that such allegations about explicit sexual content are true.
The Parkfield Parent's Community Group published a statement on the 23rd February 2019. Their main concerns were that these lessons began without parental consultation, and that they were in effect teaching children sex; a claim which appears incorrect.
The policy of the school is disproportionate, morally unacceptable and
violates the democratic rights of parents to have children educated in
consistency with their own beliefs and philosophical convictions.
One 4-year-old Parkfield child came home and said that her teacher had
said “We can be a boy or a girl” and “wear boy’s clothes or girl’s
clothes”. Another one told her mother that she learnt “boys can marry
boys and girls can marry girls.”
These are statements of legal fact. The parent's group statement affirms the right of individuals under the Equality Act to self-expression and protection from discrimination, however the distinction between education of the legal fact and "promotion" i.e. advocacy is blurred.
There are claims of specific incidents which are regarded as crossing a red line. Specifically, the claim that someone can be a Muslim and gay, and that children were asked to write "being gay is OK".
The statement does have a specific definition of promotion:
Introduction to the book: “What we now need to be teaching is that
homophobia once existed but we don’t have it in our school today, and
that to be a person who is gay or lesbian or transgender or bi-sexual
is normal, acceptable and OK. Children need to be learning that they
may identify or may not identify as LGBT as they grow up, and that
whoever they grow into as an adult is also perfectly normal and
acceptable.” (No outsiders in our school – page 2) (italics added,
this is a promotion of a homosexual lifestyle).
In this case there seems to be ambiguity on the question of promotion, as the parent's group themselves affirm the rights of individuals under the Equality Act. So this definition seems to leave more questions than answers.
EDIT: To clarify a broader cultural and legal context on the topic of toleration, as it appears this is not understood.
In the United Kingdom it is illegal to discriminate against someone because of age, disability, gender reassignment, marriage and civil partnership, pregnancy and maternity, race, religion or belief, sex, and sexual orientation.
British society's toleration is rooted in the bloody turmoil of the reformation, in which Catholics and Protestants butchered each other because they sincerely believed the other side were evil agents of the anti-Christ, and failure to do so would put their immortal souls in peril.
In 1673 the Test Act was introduced, requiring that anyone in the civil service must take communion in the Church of England. The first progressive legislation was the Toleration Act 1688, allowing Nonconformist Protestants the right to assemble and worship. However, nonconformists had to wait until the Sacramental Test Act 1828 before they could legally take public office. Discrimination against Catholics was repealed in 1829 with the Roman Catholic Relief Act.
Toleration was gradually extended to other groups. In 1967 the Sexual Offences Act decriminalised consenting relationships between adult men, the Race Relations Act 1968 ended discrimination in employment and housing, and the Sex Discrimination Act 1975 forbade discrimination by sex or marital status.
In 1988 the Local Government Act's Section 28 forbade local government from promoting homosexuality. This was repealed by 2003's Local Government Act, and later sexual orientation became part of the Equality Act 2010.
Toleration however is not afforded to groups believing in the elimination of sections of society. Groups espousing Nazi or Islamist ideology are banned and their members jailed, and similarly groups dedicated to political violence are forbidden (Northern Irish terrorism: IRA, UVF, etc).
Schools are within their rights to educate children on the cultural and legal reality of their country. This is especially important given the unfortunate reality of widespread prejudice. Official records show on average 100,000 racist hate crimes a year in England and Wales. Hate crimes against gay and lesbian people have doubled during 2013-2018 to around 12,000 incidents, while hate crimes against transgender people have trebled.