Primary schools in Manchester have been contacted by parents unhappy over sex and relationships lessons that teach children about LGBT rights, in the wake of similar classes being withdrawn in Birmingham after protests.

The Guardian understands that parents at seven primary schools have contacted school management to discuss the inclusion of the lessons in the curriculum.

Parkfield community school, in the Saltley area of Birmingham, recently hit the headlines after it became the scene of weekly protests over “No Outsiders” lessons, which parents claimed were “promoting LGBT ways of life”. The programme, which is designed to challenge homophobia, was suspended indefinitely until a resolution can be reached with protesting parents.

An academy trust in Birmingham has also suspended the No Outsiders programme at some of its primary schools. In a letter to parents seen by the Guardian, the Leigh Trust said it would not be continuing the programme at Leigh primaryin Washwood Heath until the completion of a full consultation with parents. It is understood the suspension will affect three other primary schools in the area, which are managed by the trust.

The letter stated the lessons had been suspended until the board of directors were able to have “meaningful and open discussions” with parents.

The Parkfield Parents Community group spokesman Mohammed Aslam welcomed the move. He said: “This was decided after the trust received strong objections from parents about its aims, content and misleading ‘consultations’ that preceded its introduction. The programme discriminates against the beliefs of Muslim children, parents, family values and undermines parental rights.”

On Tuesday, parents protested against No Outsiders outside Anderton Park primary school in Birmingham, although it does not run the programme.

Meanwhile, in Greater Manchester, parents at several schools, including William Hulme grammar school in Whalley Range and Acacias community primary school in Burnage, contacted the management about sex education lessons.

Although the schools in Greater Manchester do not run the No Outsiders programme, it is understood some parents, of mainly Muslim background, are concerned about the new plans to overhaul sex education lessons in schools.

In 2017, the government announced a radical overhaul of sex and relationship education and announced that children would be taught about healthy adult relationships from the age of four, with sex education made compulsory in all secondary schools. However, faith schools would still be allowed to teach “in accordance with the tenets of their faith”.

One parent, who wanted to remain anonymous and has a primary-age child at William Hulme grammar, said some parents had handed out letters on Friday urging others to sign a petition against the new sex education lessons. A WhatsApp group, which has almost 250 members, has called for protests at primary schools across the region and for parents to withdraw their children.

The parent said: “The WhatsApp group has been quite militant. It has been handled well at William Hulme’s, with the headteacher having meetings with parents, but there are lots of other schools.

“These are just regular sex education lessons – they are not like No Outsiders – but because of Birmingham they have heard that this is in the pipeline and it’s got totally blown out of proportion. Some of them don’t want their children taught about sex at all, but the main thing they are worried about is LGBT. Some people don’t want their kids being taught that it is OK to be gay.”

The parent said the headteacher confiscated the letters and had a meeting with some parents.

Another parent, who is in a same-sex relationship and has a child at William Hulme, said they felt “incredibly uncomfortable” at the prospect of protests, adding: “I am really worried this is going to gather a head of steam and it will get worse. I couldn’t bear to have a situation like you have in Birmingham where there are protests and speakers on soapboxes with microphones outside the school.

“There are already issues surrounding homophobia, and I am really supportive of how the school deals with this. It worries me because there are lots of LGBT pupils, including Muslim children, and there are certainly lots of LGBT parents … it is horrible that there are parents who don’t want their children to be taught to be LGBT is OK.”

The school pointed out it had only been contacted by five parents about the changes proposed by the government and that those discussions had been straightforward and amicable. It also stressed that there had been no reference to the situation in Birmingham in the meetings, nor protests at the school.

Angela Stansfield, the assistant headteacher at Acacias primary, said there had been no protests but some parents had requested a meeting. She said: “We are planning to do a meeting for parents later this term to explain where we are with the new curriculum … a significant issue with our parents seems to be linked to LGBT, and our approach has always been that we do not promote any particular sexuality.”

The other five primary schools in the Greater Manchester area where parents are understood to have contacted management about the lessons are Birchfields, Gatley, Plymouth Grove and Claremont primary schools and MEA Central. All of the schools have been contacted for a comment.

A Birchfields spokesman said they had held a meeting to address parents’ concerns, adding: “We have been able to reassure them that nothing has changed here and that we will fully inform them if it does.”