Christian Concern is in mediation with the Law Society after the cancellation of its traditional marriage conference on grounds of equality.
The Christian advocacy group had been due to hold their conference at the Law Society's Chancery Lane headquarters on 23 May 2012, but their booking was cancelled at the last minute after a member of the Society complained that it was an "anti-gay marriage conference".
The Society defended its decision to cancel the conference on the grounds that it breached equality and diversity policies.
Andrea Minichiello Williams, barrister and chief executive of Christian Concern said: "The cancellation of the event even meant that well respected journalists, academics and political commentators were being prevented from entering the discussion."
The mediation came on the same day as the House of Lords Committee sat to scrutinise the Same Sex Marriage Bill.
Christian Concern fears its experience with the Law Society reflects a trend to prevent views of marriage and sexuality being talked about in public, except where these support homosexuality.
Minichiello Williams warned that without strident protections for those with a traditional view of marriage, the Bill would create a society in which "it is no longer possible to talk in public about a personal belief on this issue".
"The 'censoring' of such a fundamental, foundational view which has been at the bedrock of our understanding of family life is frightening," she said.
"We enter into mediation in the hope that the Law Society will recognise that the clash of 'rights' goes to the heart of a free and democratic society, and we will work toward a just and good outcome. But across Westminster, Peers must have their eyes fully open to the implications this Bill will have at a local level in schools and charities, and on public platforms and in the media, unless specific amendments are made to provide freedom of conscience, thought and speech.
"Equal Rights are now regarded by most people as 'un-equal' rights, weighted in favour of whatever is the latest group to be courted for political gain. But equality is too valuable a doctrine to be sacrificed at the political altar. Equality is a concept which must be preserved for all, not for the few."