On the same day that MPs voted 538 to 21 for the introduction of compulsory relationship and sex education last week Muslim activists at a Birmingham school were accusing teachers of using clay models to demonstrate LGBT “sexual mechanics” with children aged four and five.

It is the latest in a series of outlandish and unproven claims that teachers at Parkfield community school, twice judged outstanding by Ofsted, have had to endure over the past six weeks. After four years of good relations with parents – 98% Muslim – the school has become the test bed of the law before it is even introduced due to its award-winning teaching on equality and diversity. Parents, backed by activists from outside the catchment area, have been holding weekly demonstrations at the school and keeping pupils out of lessons, claiming that teachers are encouraging their children to be gay.

The school strongly denies that it is teaching about sex to young children. Yet it has been advised by Department for Education (DfE) officials negotiating with parents to call off the lessons and not to issue denials or talk to the media for fear of inflaming the situation.

Hazel Pulley, Parkfield’s headteacher for nine years and now CEO of the Excelsior Trust, which has run it for the past two, told the Guardian in 2016: “Parents know that we respect Islam here and we are not in any way disrespecting it. We are saying that we are teaching is the law of our country. I tell them that whatever they say indoors is their decision but it is lovely that children will hear both views.”

Protest organisers make it clear that they are aiming to have the teaching abolished “not just in this school but at every school in Birmingham and every school in the country”. Observers warn that what is happening in Birmingham will be mirrored across England when the lessons are introduced in September 2020, unless the government stands firm on equal rights and diversity.

Parkfield appears to be teaching only what the government – and MPs – want all primary schools to tell pupils. Statutory DfE guidance in February said the new primary relationship teaching should include “different family relationships” and “the right to equality under the law for people who are LGBT”.

However, Andrew Moffat, Parkfield’s gay assistant headteacher, who drew up the award-winning lesson programme for equality and diversity, has been targeted, nicknamed “Mufti Moffat” and even had to walk into school past graffiti saying “No Gays Here.”

His “No Outsiders” lessons showing that everyone is welcome whatever their differences, have been stopped and last week he was banned from taking equalities assemblies – showing how different communities come together to help each other – after some children walked out in protest.

Homophobic incidents at the school have quadrupled compared with the same time last year, several directed at him, school sources say.

Moffat, unable to eat or sleep properly, has effectively been silenced, say his friends. Other teachers are also upset and shaking and staff absence has increased significantly. Pulley has said staff are “distraught”.

Moffat has received hundreds of messages of support by email and post – one parent even sent a hamper of cakes and biscuits to cheer him up. Though many parents at the school support him and the teaching, the un-challenged allegations are fuelling concern.

In fact, Moffat, who is in charge of pastoral care, does not take the lessons. That is done by classroom teachers with the doors open with teaching assistants – mainly from the Muslim community – present. The concern appears to be over two of the books used with children aged four and five – the first encourages pupils to think about different families. “Some families are big, some families are small …some have a step mum or dad, some adopt children … some families have two mums or two dads, sometimes they have one parent instead of two,” it says.

The second, Mommy, Mama and Me, is about a child with two mummies, showing how both can care for the child.

Ofsted carried out a special inspection last month and reported that the teaching was “age appropriate” and that most parents accepted it. It re-confirmed its “outstanding” judgment.

Moffat has been awarded the CBE for his work to promote community cohesion and last month was one of 10 finalists worldwide for the prestigious US$1m Varkey Foundation global teacher prize.

Prof Colin Diamond, of the University of Birmingham and a former deputy education commissioner, says the decision to call off the lessons is “terrifying”.

“It’s sending out the message that the curriculum is negotiable according to mob rule. I have yet to see any statement of unequivocal support for the school from the DfE. Headteachers working further afield where the protests have spread, such as Oldham and Manchester, are vulnerable unless they can count on local and national support,” warns Diamond, a former deputy education commissioner for Birmingham.

A spokesperson for the Department for Education said: “We want children to know that there are many types of relationships – that’s why we are making relationships education compulsory in all primary schools from 2020. This will ensure pupils are taught the building blocks needed for positive and safe relationships of all kinds – starting with family and friends – and how to treat each other with kindness, consideration and respect.

“Following the introduction of the new regulations, there is time for schools to consult parents on how the new subjects will be taught. Schools talk to their parents all the time so we trust head teachers to take the decisions as to what is appropriate for their pupils to be taught.

“No school or teacher should face undue pressure from outside their school communities. The department will do all it can to support headteachers to do their jobs, free from intimidation.”

• This article was amended on 2 April 2019 to add a response from the Department for Education that was received after the production deadline.