Religious leaders have spoken out against abolishing faith schools
The Lib Dems have voted in favour of allowing state-funded faith schools to continue selecting pupils by faith.
The party has also rejected calls to ban the setting up of new state-funded faith schools in a vote at its spring conference in Harrogate.
But schools which could not demonstrate a commitment to inclusiveness in their intake would face funding cuts under the Lib Dem plans.
The opt-out from equalities legislation for faith school staff would also end.
But there would be an exemption for staff who are responsible for religious instruction.
Pupils who are "old enough to decide for themselves" would also be allowed to opt-out of faith-based school assemblies, under the Lib Dem plans.
Many Lib Dems, including frontbench figures, believe faith-based admissions can be socially divisive.
But others, including deputy leader Vince Cable, argued, during an impassioned debate, that they must be a feature of a tolerant society.
Some party members argued it would not be realistic to ban them, given that they represent a third of schools in the UK.
On Friday, representatives of the Anglican and Catholic churches and Jewish, Muslim, Hindu and Sikh faiths signed a letter to the Guardian newspaper saying that banning selection of pupils by faith in religious schools would be "perverse and unjust".
The party leadership is keen to promote its education and family policies at the weekend conference.
Lib Dem members also voted to cut class sizes for infant school children, aged between five and seven.
They want them to be reduced to private school levels of about 15 per class and to plan to spend £2.5bn on closing the gap between children from rich and poor backgrounds.
They also backed scrapping the 600 page national curriculum and replacing it with a slimmed-down minimum curriculum entitlement and setting up an independent Education Standards Authority to restore confidence in standards.
The party's education spokesman David Laws said: "Our plans would slash class sizes in infant schools - where small class sizes matter most - and boost funding for the children who need it most.
"Our Pupil Premium would bring the funding of the most disadvantaged pupils up to private school levels."