About a third of schools in England are faith based
A majority of people in the UK believe offering school places on grounds of religion is likely to undermine "community cohesion", claims a survey.
The Accord group, which campaigns against faith-based admissions, found 57% agreed with its suggestion that choosing by religion could be divisive.
The group accuses some faith schools of "exclusivity and insularity".
The Department for Children, Schools and Families said all English schools had a legal duty to promote cohesion.
And the department says that in practice faith schools have a higher proportion of ethnic minority pupils than other types of state school.
The survey from Accord asked a representative sample of adults whether they agreed that "state funded schools that select students by their religion undermine community cohesion".
It found that 57% either agreed or strongly agreed. And 72% said schools should not have employment policies that "discriminate on grounds of religion or belief".
The chair of Accord, Rabbi Jonathan Romain, said: "It is time for faith schools to open their doors to the fresh air of inter-communal understanding. They must not only serve themselves but be part of the wider community too."
Faith schools, when they are oversubscribed, can use religion when allocating places along with other factors such as distance, aptitude or whether siblings already attend.
About a third of state schools in England are faith schools - a majority of these being Church of England and Roman Catholic, with a smaller number serving Jewish, Hindu, Sikh and Muslim communities.
A joint letter written on behalf of faith school representatives earlier this year said it was "perverse and unjust" to attack such a popular and successful part of the state school sector.
"We believe that parents and students should continue to have the right to choose the type of school in which they can flourish academically, socially and spiritually."
England's education department, which has said it will create more faith schools where there is parental demand, rejects the claims that they could weaken community cohesion.
"All maintained schools, including faith schools, have a legal duty to promote community cohesion - and Ofsted specifically inspect them on this.
"The fact is that faith schools tend to be more ethnically diverse than non-faith schools.
"The admissions code prohibits selection and unfair admissions practices which can increase social segregation."
Only 14% of Scotland's state schools are faith schools - almost all Roman Catholic.
"We believe it's important for parents and pupils to have the choice to attend a faith school, if they want to," the Scottish Government says.