Protesters branding school lessons about LGBT rights as "toxic" and "disgusting" have been accused of using "appalling" and "incendiary" language.
It follows footage of continuing rallies at a Birmingham primary school where the lessons have been taught.
A man can be heard telling a crowd outside Parkfield Community School that teaching about social difference is "aggressive indoctrination".
Police are reviewing the video to see whether any offences are committed.
The footage - in which a vocal and supportive audience is told homosexuality is incompatible with Islam - was taken outside the school.
On Thursday, Birmingham City Council's cabinet member for social inclusion John Cotton said: "In recent days, we have been appalled to see attempts to divide the people of our city by using insulting and incendiary language targeting the LGBT community."
While Parkfield is an academy, not a local authority school, Mr Cotton said the council was monitoring the situation.
Neither the school nor the protesting group, which includes parents of pupils, wished to comment.
Calling for the police to step in, a spokesperson for the Naz and Matt Foundation, a charity which tackles "homophobia triggered by religion", said the video showed "incitement of hatred".
A statement added that "encouraging children and parents to publicly shout 'shame, shame, shame' outside of a primary school towards those inside is not acceptable".
West Midlands Police said no formal complaints had been made to the force, although it was investigating homophobic graffiti on the school premises.
A spokesperson said: "Video footage circulated on social media is being reviewed to establish whether any additional offences have taken place."
The school in Alum Rock has about 740 pupils aged three to 11 and has been teaching the lessons under a programme called No Outsiders which, in addition to LGBT rights, covers other diversity issues including race and religion.
It says the lessons teach pupils how to recognise and celebrate difference.
The lessons have stopped, but the school says it is not a u-turn, but part of a pre-existing plan to focus on religious education for the rest of the term, with No Outsiders to remain part of its ethos.
Parkfield is not a faith school, but some protesting parents have complained the teaching is incompatible with pupils' religion.
People representing multiple faiths are reported to have protested at the site, although the video footage features complaints the lessons jarred with Islam.
The crowd was told on Thursday the lessons taught pupils "it is okay for you to be Muslim and for you to be gay".
They also heard it was "aggressive indoctrination" of children and an attempt to change religious beliefs - with the teaching then branded "toxic" and "disgusting".