A new report by the leading charity – backed by a legal opinion from a leading QC – says the Bill will make it impossible for all churches and faith-based charities to insist that their senior staff lead private lives in accordance with their religious beliefs.
CARE said that, under the Bill, which will be considered by the House of Lords on Monday, it would be illegal for a Christian charity to sack a senior manager for adultery or living an openly gay lifestyle.
The same rules would, it added, apply to Muslim and Jewish churches and charities.
However, the biggest potential showdown is likely to be between the government and Britain's 4.3 million Catholics over the church's tradition of an all-male, celibate priesthood.
Previous legislation in 2007, also backed by Ms Harman, the Commons Leader and equality minister, forced the closure of two Catholic adoption agencies for refusing to comply with new laws requiring them to place children with gay couples.
CARE's report – A Little Bit Against Discrimination? – warns that the proposals contained in the Bill are a serious threat to religious liberty in Britain.
John Bowers QC said in a legal opinion for CARE that the Bill could make it unlawful for a church to require a priest or minister to be male, celibate and unmarried, or not in a civil partnership.