A "homophobic" video and far-right material linked to protests against LGBT relationship lessons are being investigated by police.
The clip - circulated via WhatsApp - claims primary schools are teaching Islamic children about sex and warns of a "campaign against Muslims".
It has also emerged that anti-Islam material was sent to one Birmingham school at the centre of the protests.
There are now fears the row is "being exploited" by two sets of extremists.
"We believe both Islamist and far-right activists are using the protests to foster division between communities," said an officer for counter-terrorist scheme Prevent, who asked to remain anonymous.
West Midlands Police said it was reviewing "a large amount" of material.
No arrests have been made.
The video refers to protests against relationships and sex education (RSE) lessons held earlier this year in Birmingham where at the demonstrations' height, Anderton Park Primary School was scene to hundreds of mainly Muslim campaigners.
They said the teaching was incompatible with Islam.
The social media footage was reported to police by the school's head teacher Sarah Hewitt-Clarkson, who described it as "homophobic".
She told BBC Newsnight: "I think it's a police matter because it's clearly homophobic, it incites hatred towards gay people."
She branded claims children were taught about "any kind of sex" as "ridiculous".
Ms Hewitt-Clarkson said the school had also received anti-Muslim and far-right material, which she referred to Prevent and the West Midlands force.
The row over RSE - which becomes compulsory from September 2020 - has spread to other cities.
The head teacher of a London primary school - who wished to remain anonymous - told Newsnight more than 100 children at her school had been withdrawn from similar classes.
Last year "only a handful" were taken out of lessons, she said.
'Children's homophobic comments'
She said the majority of parents who objected were Christians.
The backlash had made her concerned for pupils' safety, she said.
"I've seen a change in behaviour of particular children being homophobic in their comments towards others in the playground," she said.
Birmingham Labour MP Jess Phillips told Newsnight the advent of compulsory RSE teaching was a an excuse for "hardline" protests.
She said: "This has happened because a mixture of very far right, radical, and very hardline religious people have started a campaign and the Department for Education is allowing that campaign to go on because it's being lily-livered."
The Department for Education said RSE was a "vital" subject and schools would be supported to deliver lessons "to a high standard".
It said it was working closely with schools that had volunteered to introduce the subject next month, and was setting up a working group including parents, young people and representatives of faith and minority groups to consider the delivery of the lessons.
Parents with concerns were urged to "talk to their child's school in a calm and constructive way".