The directive, by Waltham Forest and Newham councils, in east London, even affects schools where very few pupils are Muslim, Hindu or Sikh.
After concerns were raised, a review of the policy has been launched in Waltham Forest, with some criticising the closures as inappropriate, unnecessary and "political".
Headteachers have argued that they should be given discretion in deciding which days to mark, as happens in big multi-ethnic cities including Manchester, Birmingham and Bradford.