New legislation outlaws employment discrimination on many grounds
Churches have warned new equality laws could force them to go against their faith when hiring staff.
They say the Equality Bill may force them to employ sexually active gay people and transsexuals when hiring staff other than priests or ministers.
Churches currently have special status allowing them to turn down certain candidates for ministers or priests.
The government says it is not trying to narrow the churches' ability to employ lay people who share their values.
The Equality Bill - which is due to be debated in the House of Lords on Monday - would allow churches to avoid appointing homosexuals to clerical roles.
However, some bishops claim that they could lose the right to ensure other important staff - such as key representative and teaching roles - had lifestyles compatible with church beliefs.
Three Anglican bishops have written to members of the House of Lords, appealing to them to vote against what they see as a weakening of the churches' special status under the Equality Bill.
A statement was issued on behalf of the Bishop of Winchester, the Right Reverend Michael Scott-Joynt, the Bishop of Exeter, the Right Reverend Michael Langrish, who is Chair of the Churches Legislation Advisory Service, and the Bishop of Chester, the Right Reverend Peter Forster.
They said the issue involved striking "the right balance between the rights and responsibilities of different groups to be protected from harassment and unfair discrimination and the rights of churches and religious organisations to appoint and employ people consistently with their guiding doctrine and ethos".
The statement went on: "The Christian churches, alongside many other faiths, support the Equality Bill's wider aims in promoting fairness in society and improving redress for those who have suffered unjust treatment.
"However, unless the present drafting of the Bill is changed, churches and other faiths will find themselves more vulnerable to legal challenge than under the current law."
Churches are allowed to turn down candidates for jobs as ministers or priests if they are actively homosexual or have changed their gender, or if they are women.
Bishops claim that the exemption currently extends to key staff such as youth workers or the heads of Catholic schools.
They say that changes proposed by the government would remove it.
Keith Porteous Wood from the National Secular Society believes the bishops' position is "entirely unreasonable".
He told BBC News: "For every discrimination there's a victim, and it seems entirely unreasonable that the churches should be permitted to discriminate, on grounds of sexual orientation, against administrative staff, janitors, other ancillary staff - given that an EU directive does not permit them to be discriminated against."
Meanwhile, a Church of England spokesman looked forward to the bill being discussed.
He said: "The Lords Spiritual play a valuable role in politics in the UK and the debate will be further enriched by the opinions of others in the House of Lords."