Libby Powell, from campaign group Christian Concern, appeared on BBC Three Counties Radio on November 3.
During an interview with comedian and presenter Iain Lee she was called a bigot after she said homosexuality is a sin.
Ms Powell was discussing the case of Revd Barry Trayhorn, a prison worker taking his employer to a tribunal amid claims he was forced to resign for reading a Bible verse about homosexuality.
Iain Lee said Revd Trayhorn was "obnoxious" and "poisonous" and said his views, and Ms Powell's were homophobic.
When Ms Powell said homophobia was a fear Mr Lee said it was a "cute answer" but homophobia was a "hatred of gays".
He asked if Revd Trayhorn would embrace gay people and was told by Ms Powell that he would.
"Bit gay," replied Mr Lee.
The BBC admitted the language the presenter used, and the tone in which he conducted the interview, was "at several points inappropriate".
A statement from senior editorial staff said: "The BBC - and Iain Lee himself - wish to apologise for any offence that may have been caused."
Iain Lee apologised on air and said: "Last week I interviewed the Revd Barry Trayhorn and solicitor Libby Powell about their understanding of biblical teaching on homosexuality.
"I want to make it clear that I apologise for any offence that may have been caused over the way I conducted the interviews."
Christian Concern had labelled the interview "intolerant" and asked its supporters to complain.