Church schools cannot be "anti-gay marriage" the government's integration chief has warned.
Dame Louise Casey, head of the Prime Minister's review into community intergration, told MPs "it is not okay" for church schools to teach marriage is between one marriage and one woman.
She warned such a view was "often veiled as religious conservatism" but in reality was "homophobic".
Casey, who formally ran the government's Troubled Families programme, warned religious extremists were infilitrating schools in a similar way to the Trojan horse scandal.
"It is happening elsewhere," she said but went on to say that she saw extremism in other areas apart from Islamic fundamentalism.
Giving evidence to MPs on the communities and local government select committee on Tuesday, she said: "I have a problem with the expression 'religious conservatism', because often it can be anti-equalities.
"We have got to be careful that people can choose, obviously, to live the lives that they want to live, but that they cannot condemn others for living differently.
"That is a grey line, and the more we can talk about it the better. That is the most important thing: that people are able to talk about it."
Casey's year-long review published in December found successive governments have failed to ensure cohesion keeps up with the "unprecedented pace and scale of immigration", which has left some communities increasingly divided. She found racial segregation and social exclusion have reached "worrying levels" in the UK.
Casey put a spotlight on Muslim-majority areas, noting that some mosques teach women and girls regressive ideas about their role in society. She warned the fear of being labelled racist had led to public bodies ignoring or even condoning divisive and harmful religious practices.
She told MPs on Tuesday: "Everybody is frightened of being branded a racist - there are some nasty people on the right who clearly aren't - but most normal people are frightened of being branded a racist.
"The very genuine fear in all of this is we have two extremists alive in our communities. We do have the extreme right wing which is milking all of this for its worth.
"We have extreme right wing in our country which we are all utterly appalled by.
"But we also have Islamist extremism at play and I have felt at points it has been easier to talk about one than it is to talk about the other.
"It is a disservice to thousands of people caught up in actually being on the receiving end of not having the start in life they should have in the UK."
The Coalition for Marriage campaign group said her remarks were "astonishing" and "one of the clearest indications" that those backing traditional marriage were seen as extremists.
"Believing that marriage is between one man and one woman doesn't make you homophobic or an extremist. It's Dame Louise Casey's comments which are extreme," a statement read.
