Over the past few weeks, we have reported growing concerns about a possible backlash against faith schools, following the so-called "Trojan Horse" inquiry into Islamist indoctrination in a number of state schools this summer.

Recent events can only have reinforced those fears. Since the start of July, three of the country's 12 state-aided Jewish schools and academies have received no-notice visits from Ofsted inspectors; the downgrading of one of them, JFS, from an outstanding school to one that "requires improvement" was thought particularly harsh by many in the Jewish community.

Then Education Secretary Nicky Morgan proposed forcing schools to teach more than one faith for GCSE religious studies in a move opposed by Chief Rabbi Ephraim Mirvis.

But the most serious outcry has come from the National Association of Orthodox Jewish Schools (Najos), a group representing the more right-wing religious sector, which accused the inspection service of bullying pupils with insensitive and anti-religious questions.

Girls in a strictly Orthodox secondary school were asked by inspectors if they knew about gay marriages, had boyfriends or used social media, according to Najos. Even nine-year olds in a primary school were reportedly asked if they knew any gay people and how babies were made.

One of the schools that was subject to an unannounced inspection, Beis Yaakov, a girls' secondary school in Salford, is understood to have formally complained to Ofsted, although neither party will confirm this.

But anxiety is not confined to Jewish schools. Ofsted was forced to withdraw a critical report that a Catholic secondary school had not done enough to make pupils aware of extremism after the school complained. Only this week, the evangelical Christian Institute claimed that inspectors had told a Christian independent school that it should invite an imam to take assembly to promote interfaith goodwill.

In the face of criticism, Ofsted says that it is not looking to undermine children's own religious traditions but that it does expect them to display views "neither intolerant nor discriminatory towards others".

Post-Trojan Horse, the government's wish to root out Islamist radicalism has led to new guidelines to strengthen the teaching of "fundamental British values" in schools. They are meant to foster "tolerance and respect for people of all faiths (or those of no faith), cultures and lifestyles".

Proposed revisions to the inspection of independent schools , for example, would enable the education authorities to act against institutions which fail to "address homophobia" or to challenge prejudice against other faiths.

Although the Board of Deputies believes that there is no contradiction between Jewish values and British values, it does think Ofsted may be overstepping the mark in its interpretation of the guidelines.

The Board also stresses that head teachers have the right to ask inspectors about what kind of questions they intend to put to children in advance and object if they think these would contravene the school's religious ethos.

One strictly school Orthodox school representative said that children would be taught that it was wrong to bully people in general, but that it would not talk about homophobic bullying as such.

No Orthodox school would teach that gay or lesbian sexual relationships were a valid alternative in Judaism; but expecting children to know about gay marriages - as some inspectors now seem to be doing - marks a curb on the freedom long enjoyed by faith schools.

Najos will have the chance to explain its case when it meets Ofsted next month. Only a few weeks ago an inspector turned up unannounced at one Jewish school on the afternoon of Rosh Hashanah - although the visit was postponed when the timing was pointed out. A Chasidic primary school whose pupils would have no access to the internet was also recently criticised for not having a policy on cyberbullying. If the inspection service wants to encourage respect for diversity, it should perhaps demonstrate greater cultural awareness first.