Bosses at the corporation decided to get rid of the role in a bid to save money during restructuring.
In a joint open letter with Jewish and Muslim leaders Rt Revd David Walker said the BBC's religion provision was an "antidote to extremism and intolerance".
He added that "religion is not history" and urged the BBC to reconsider.
"From religious efforts at tackling Ebola in West Africa, to the interfaith solidarity that has so far helped prevent the horrors of France being imported to these shores, religion remains a force for change at home and abroad.
"Religious literacy is essential to the diversity we treasure in Britain - and a tonic to the extremism and intolerance that threaten it.
"The BBC plays a key role here, providing robust and rich coverage of religious life to the British public."
The letter is jointly signed by Rabbi Laura Janner-Klausner, leader of Reform Judaism in the UK, the Secretary General of the Muslim Council of Britain, Dr Shuja Shafi, and the Bishop of Manchester.
A BBC spokesperson said: "The BBC's commitment to Religion & Ethics output is unequivocal.
"The proposed restructure of Factual commissioning will deliver significant savings and increase creativity and collaboration, enabling the best ideas to get on screen. Aaqil Ahmed's role as Head of in-house Religion & Ethics Production is not affected by the restructure."
