The Church of England wants all faith schools exempted from a planned ban on discrimination against homosexuals.
The church predicts potential legal challenges
In its response to a government consultation, the church says it makes a distinction between people's sexual orientation and their behaviour.
Schools would not want to discriminate in admissions, opportunities or discipline, the paper says.
But they would want to deliver the curriculum "in a way that is consistent with their school's ethos".
A Liberal Democrat MP, Evan Harris, said schools were not the place for religious moralising about sexual orientation.
"Religious organisations need to understand that they must save that for the pulpit, not the classroom," Dr Harris said.
"It is completely wrong for educational establishments, particularly those that are state funded, to be exempt from the requirement not to discriminate on grounds of sexual orientation."
In its response to the government plans, the Church of England said: "Church schools do not seek actively to convert children but to provide an experience of what it is to live in a community that celebrates the Christian faith."
But the way the proposed regulations would apparently have an impact upon the curriculum in all state schools.
Issues could be raised as to whether the content of worship or sex education was consistent with them.
The current framework said pupils "learn the nature of marriage and its importance for family life and the bringing up of children".
It did not exclude the need to recognise the value of other stable relationships.
Schools had to ensure the needs of all pupils were met, and the direct promotion of sexual orientation was not allowed.
The church argued that a general duty not to discriminate would mean changing that framework.
It "would not only fail to offer any significant additional benefits, but, more seriously, would expose schools to a real risk of costly legal challenges".
"That seems highly undesirable," it said.
Faith schools - of any sort - could find a conflict with their need "to operate in a way that is consistent with their school's ethos".
Current sex education guidance from the Department for Education and Skills let schools teach in a way that was consistent with their ethos, it said.
"Whilst recognising that pupils must form their own views and beliefs, and respect themselves and others, church schools would wish to retain that freedom, which is central to their role."
Faith schools might also be required to make their premises equally available to groups whose purposes were "inconsistent with their ethos" - upsetting staff and parents.