The National Secular Society has accused Ofsted of "capitulating to oppressive religious demands" after the schools regulator told inspectors that gender segregation in faith schools should not be taken as a sign of inequality.

In recently updated guidance on inspecting publicly funded "faith schools", inspectors are advised that in Muslim faith schools: "boys and girls may well be taught or seated separately according to the specific context, particularly during collective acts of worship. This should not be taken as a sign of inequality between different genders."

The guidance also cautions inspectors to be mindful to not misinterpret the wearing of the 'hijab' or headscarf as a sign of repression but instead to "understand that Muslim females see this as a part of their identity and a commitment to their beliefs within Islam".

The guidance says most schools have a uniform for boys and girls which represents the "Islamic principle of modesty".

Inspectors are advised that art and music lessons in Muslim schools can be "restricted", that health and sex education will be taught within Islamic studies and that daily prayers will often "dictate the shape of the school day".

In a section on "etiquette", female inspectors are advised to "wear a trouser suit or longer skirt and jacket to cover their arms". Female inspectors are also recommended to "carry a scarf in case they enter the prayer room".

According to the guidance "Muslim men do not usually shake hands with women, and Muslim women do not shake hands with men". Ofsted advise the "best policy is not to offer to shake hands unless someone offers their hand to you".

It says inspectors also need to be aware that they may find themselves providing feedback from a lesson to a teacher that may be wearing a full 'niqaab' (face and head cover). In some schools male inspectors are told they will need another female present in order to give feedback to a female teacher.

The guidelines lay down that when inspecting single-sex religious schools, the inspection team should "reflect the gender of the school".

In mixed sex Jewish schools, inspectors are told that boys and girls are "in reality" taught separately – sometimes on two different sites some distance from one another.

When inspecting Jewish schools female inspectors are advised to wear a skirt rather than trousers and a blouse, but that any blouse worn should cover the collar bone. When inspecting strictly ultra-orthodox schools, inspectors are warned to "avoid wearing bright colours, and red in particular".

The guidance appears to be at odds with Department for Education policy. A spokesperson for the DfE, said: "We are clear that segregation in the classroom is wrong. The Equalities Act applies to all types of school and it is unlawful for schools to discriminate against a pupil by treating them less favourably because of their sex."

The National Secular Society called on Ofsted to review its guidance.

Keith Porteous Wood, NSS executive director, said: "These guidelines reveal a disturbing capitulation to oppressive religious demands in publicly funded schools. It also highlights the extent to which religious identities are being foisted on young people whilst at school.

"The guidance serves to normalise practices inconsistent with values such as personal liberty and gender equality, which should be promoted in schools, not eroded.

"The apparent willingness to sacrifice the National Curriculum and sex and relationships education in order to accommodate religious dogma betrays children's rights and poorly equips pupils for life outside the school gates."