Some schools are being used by individuals to "indoctrinate impressionable minds" under the guise of religious belief.
The head of Ofsted says inspectors are increasingly coming across those who want to "actively pervert" the purpose of education.
Amanda Spielman will use a speech to a Church of England education conference to warn schools that they should not assume that the "most conservative voices" of a particular faith group speak for everyone.
While insisting that many faith schools are good at promoting tolerance she will say say there is a difference between respect for others and "privileging all belief above criticism."
Ms Spielman will say some individuals want to narrow students' horizons.
"Under the pretext of religious belief, they use education institutions, legal and illegal, to narrow young people's horizons, to isolate and segregate, and in the worst cases to indoctrinate impressionable minds with extremist ideology.
"Freedom of belief in the private sphere is paramount, but in our schools it is our responsibility to tackle those who actively undermine fundamental British values or equalities law.
"That doesn't just mean Ofsted, but everyone involved in education.
"Rather than adopting a passive liberalism, that says 'anything goes' for fear of causing offence, schools leaders should be promoting a muscular liberalism,"
She will also give her backing to Neena Hall, the headteacher of St Stephen's primary school in east London, who was forced to reverse plans to ban young pupils from wearing the hijab in class.
More than 19,000 people signed a petition against the ban.
Ms Spielman will say: "Schools must not allow pressure from certain elements of school communities to dictate school policy, nor should we allow vocal parental minorities to pressure other parents and children to act or dress against their
"Giving way to the loudest voices is the opposite of tolerance.
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"It is a matter of deep regret that this outstanding school has been subject to a campaign of abuse by some elements within the community.
"I want to be absolutely clear, Ofsted will always back heads who take tough decisions in the interests of their pupils."