Leaflets claiming that new relationship education lessons will encourage primary school children to masturbate have been handed out in east London, the BBC has learned.
It comes after protests in Birmingham against LGBT teaching made headlines.
Other leaflets said parents "will be questioned on the day of judgement" if they do not challenge the lessons.
Labour councillor Rohit Dasgupta said local officials had a "duty" to counter the "misinformation".
The School Gate Campaign - which distributed the leaflets - has now removed the specific accusation that infants would be "encouraged to masturbate" in its literature, but Mr Dasgupta argued the damage had already been done.
The new flyers say some teaching resources will introduce words like masturbation to juniors. This is written in draft teaching guidance for at least one local authority in England.
The campaign said it stood by the leaflets' other claims - including that relationships education lessons would promote "transgenderism and homosexual lifestyles".
From September next year it will be compulsory to teach relationships education in primary schools in England, and relationships and sex education (RSE) in secondary schools.
The government wants primary schools to include teaching about things like single parents, adoption and same-sex relationships - but said it will be for individual schools to decide what is "age appropriate".
The proposal has led to leafleting campaigns and hundreds of mainly Muslim campaigners protesting at the gates of some primary schools, most notably in Birmingham.
There were fears the row was "being exploited" by Islamist and far-right activists.
Some parents there objected to a set of teaching resources called No Outsiders, which includes stories about a boy who wants to dress as a mermaid, and a penguin who has two fathers.
With the new school term approaching, Mr Dasgupta described the leaflets being handed out in his area in Newham, east London, as a form of "intimidation" and containing "untruths".
He showed the BBC's Victoria Derbyshire programme an example that claimed RSE would promote "transgenderism and homosexual lifestyles" and "pervert the course of natural child development".
It added that "children in infant school will be encouraged to masturbate. First sexual experiences will be encouraged by the age of 12."
Mr Dasgupta said parents had also been targeted through messaging apps, with many being told there would be "consequences" if they did not attend an upcoming parents' meeting about RSE.
Asked why it was not legitimate for parents to want a say in their child's education, he said while they should be "told exactly what their children are taught", head teachers should ultimately decide, as the experts. He added the government should have the "backbone" to support them.
"This is about making sure we teach our children about equality," he said.
The School Gate Campaign said "the majority of parents do not agree with the current approach to sex education, which demands ever more explicit sex education at ever younger ages".
Antonia Tully from the Safe at School campaign said the new legislation involved the government taking from parents "the role that is rightfully theirs".
"Parents are the primary educators of their children and they should be the ones talking to them about the intimate details of sex and about different sorts of relationships when they feel they are ready," she said.
Javid Iqbal, whose children and grandchildren have both attended Parkfield School - the centre of the Birmingham protests - is now calling for the protests to stop.
He used to speak on behalf of the Parkfield Parents Group, but said the demonstrations were "not helpful at all".
"We're adults - we're educated enough to sit round a table to resolve these issues instead of standing outside a school shouting and screaming."
Mr Iqbal also criticised those from outside the local community who had become involved in the local dispute, saying they were "just here for publicity".
Earlier this month the BBC reported that a "homophobic" video and far-right material linked to protests against LGBT relationship lessons were being investigated by police.
Mr Iqbal said "a lot of parents" had removed their children from the school to look for alternatives in the area, unhappy at how it had managed the situation.
Yehudis Fletcher, founder of Nahamu, a think tank addressing extremism in the Jewish community, has spoken out publicly in favour of the lessons, and said others had contacted her to say they supported her viewpoint but did not wish to voice it openly.
She said this was because there was "such a loud opposition... and fear of putting your head above the parapet".
Ms Fletcher, an orthodox Jew who has three young children, said some of those running orthodox schools in the area did not want to teach RSE.
"There are people who want children to remain largely ignorant about sex and relationships because they want them to carry on with the traditional way, in which they're married at a very early age without much knowledge of what they're getting into," she said.
The Department for Education has said RSE is a "vital" subject and schools would be supported to deliver lessons "to a high standard".
It said it was working closely with schools which 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".