Excerpt:
The National Union of Teachers (NUT) said the move would be a way to reunite divided communities.
The NUT said parents had a right to have specific schooling in their own faith, if that was what they wanted.
But the Church of England disagreed, saying: "Religious instruction belongs with the religious institutions."
'Not about indoctrination'
A Church of England spokesman said: "It is for religions to teach their faith to people; it is for schools to teach about religion.
"Faith schools are not about indoctrinating children in a particular faith."
He added: "Church schools are generally welcomed by parents, which explains why they tend to be over-subscribed."
But the NUT said having children taught at different faith-based schools had led to community breakdown in some areas.
Offering pupils some instruction in their own faith could reduce the demand for faith schools, said NUT General Secretary Steve Sinnott.