The liberal Democrats agreed a policy on faith schools for the first time in nearly 10 years at the party's spring conference in Harrogate last weekend.
The policy calls for a greater inclusivity from faith schools in their admissions or risk losing state funding.
The party also voted to abolish their right to opt out of employment and equality legislation, which enables religious schools to employ staff on the basis of their faith.
Speaking after the school policy paper was voted through, David Laws, the Lib Dems' education spokesman, said that it was "enormously important" for the party to have a standpoint on faith schools.
"Most faith schools are happy to be more inclusive, but there are areas where children have no alternative other than the local faith school. If they are not of the same faith then they will not be able to attend their local school, which we don't think is fair," he said.
"On employment, we believe the religious instruction should be upheld to carry on the school's ethos, but a good physics teacher or a headteacher should not be denied a job because of their faith."
Under the policy, faith schools would be given five years to show their plans for inclusivity to the local authority, which would have the power to remove a school's state funding if its proposals were not satisfactory.
The Muslim Council of Britain said faith schools were "active when it came to inclusivity", but warned that schools could be undermined by headteachers who were not of the faith.
Tahir Alam, a council education spokesman, said: "Excellent teachers are often employed in faith schools regardless of their religion, but I don't think employing a headteacher of another faith would be a helpful way of supporting a school's ethos. The scenario of an atheist running a Catholic school is a joke."
The Catholic Education Service was also concerned by the Lib Dems' stance.
Oona Stannard, CES chief executive, said: "We are disappointed that the party would elect to end the right of new schools of a religious character to select their pupils on the basis of faith or belief.
"We are also concerned that it would remove the existing employment and equality legislation used to appoint Catholic staff to posts where promoting and maintaining the ethos and identity of a school and its religious character is part of the role of the specific staff member."
Morasha Jewish Primary School in north London opened in September and is applying to become part of the state sector, but this would be difficult under the Lib Dems' policy.
Ian Kamiel, the school's chair of governors, told The TES: "We would obviously have to meet the regulations that the local authority put in front of us, but we think it would be clear what type of education and ethos would be at the centre of the school, so the choice would be for the parent."
The Lib Dems' policy was agreed the day before Ed Balls, Education Secretary, called on Ofsted to carry out an investigation into independent faith schools.
It is understood the survey will examine how schools are meeting pupils' spiritual, moral, social and cultural development.
- Allow parents to choose faith-based schools and permit the establishment of faith schools in the state sector.
- Faith schools should demonstrate admissions inclusivity within five years and empower local authorities to approve their plans; cut state funding where inclusivity is not demonstrated.
- End the opt-out from employment and equality legislation for faith school staff, except those responsible for religious instruction.
- Require any act of collective worship - for example, during assembly - to be optional for pupils old enough to decide for themselves whether to attend.