Christian campaign groups, Roman Catholic bishops and other church leaders say the Equality Bill could force them to go against their faith when employing staff. They also warned that the law could lead to increased legal action between churches and atheists.
However, the government insists that the bill simply "clarifies" the current law.
A spokesman for the Government Equalities Office said: "In the case of ministers of religion and other key jobs that promote and represent religion, the bill recognises that a church may need to impose requirements regarding, for example, sexual orientation."
But church leaders are concerned that they would no longer be able to turn away candidates with incompatible lifestyles for other roles such as teaching.
They say the government has tabled an amendment to modify the bill's wording but the concession does not go far enough.