The BBC was accused of censorship on Thursday after its BBC3 debate show Free Speech dropped a question about being Muslim and gay at the request of the mosque where it was being filmed.

The live show, hosted by Rick Edwards and featuring a panel including government minister and Lib Dem peer Susan Kramer, broadcast a pre-recorded question by Asifa Lahore, self-described as Britain's "first and only gay Muslim drag queen" who asked: "One question I would like to ask the Muslim community is, when will it be right to be Muslim and gay?"

Edwards, who introduced the programme as "the show which makes your voice heard in the national conversation", interrupted before any of the panel or studio audience had a chance to respond, saying the question had been dropped in response to the concerns of Birmingham Central Mosque.

"We were going to debate that question but today after speaking to the mosque they have expressed deep concerns with having this discussion here," said Edwards. "They were happy for us to play that video and we will talk about it on our next programme on 25 March."

Some of the programme's 79,000 viewers complained about the decision on Twitter, using #freespeech censorship. Produced by Mentorn, the makers of BBC1's Question Time, the Free Speech website says: "Britain is a democracy where we can say what we want. So let's say it."

Stephen Evans, campaigns manager at the National Secular Society, said: "After agreeing to allow a programme called Free Speech to be filmed at the mosque, it is absurd and counterproductive to then censor the topic being discussed."

He added: "Perhaps the BBC would do well to choose religiously neutral venues to hold such debates in future."

In a statement, a spokesman for the programme said: "BBC3's Free Speech is determined to discuss the issues that matter to its viewers. However, out of respect to the Birmingham Central Mosque, who hosted the programme on Wednesday 12th March, the decision was made to delay the debate on Muslim gay rights to a future programme.

"The topic will be raised and debated in full on the edition of Free Speech airing on March 25th."

The BBC announced last week that the BBC3 TV channel is to be axed, with the youth brand going online only from the autumn of next year.