Core Issues Trust (CIT) requested for Voices of the Silenced to be shown in a private invitation-only event at The Queen's University Belfast.
However, the Christian charity in Northern Ireland said its request was declined "without reason".
Joan Parsons, Head of Queen's Film Theatre (QFT) at the university told the charity: "The mission of the Queen's Film Theatre (QFT) is to widen access to film through the delivery of a varied programme that actively encourages appreciation, enjoyment, debate and understanding.
"In addition, the QFT is committed, through its approved programme, to continue to promote and respect equality, diversity and inclusion."
It is not clear how the film fails to meet the theatre's mission.
The film has sparked controversy since it was premiered last month.
Vue Piccadilly cinema scrapped a reservation for the screening of the film, which tells the stories of 15 people "emerging out of homosexual lifestyles" after more than six hundred people signed a petition urging the cinema chain to cancel the private showing, which 125 guests had been due to attend.
However, the premiere went ahead when producers were offered a conference room at the Emmanuel Centre in Westminster instead.
Challenging the university's decision, CIT's CEO Mike Davidson said: "Clearly in Northern Ireland, in line with the rest of the UK, Christian freedom is restricted to freedom of worship alone. It is an illusion to believe that Christians have freedom of religion or even freedom of conscience.
"If it is up to the politicians and the leaders of our institutions, Christian values have no place in the public space, which is reserved for the dogmatic religion of secularism, and promotion of LGBTI values which alone define diversity and inclusiveness.
"More dangerously, homosexual identity in the UK appears now to be mandatory for those experiencing the feelings. It seems there may be no dissent; gay identity must be affirmed and there is no debate to be had about the matter. But this is exactly why the politics of sexuality are unsustainable and will unravel."
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