The church has said the recital is a Pride event, which the choir strongly denies.
Speaking on Today with Claire Byrne, Chairman Patrick McNamara, said: "It is our annual summer concert that we do every year in June and we do in different locations around Dublin and happens to be this year built into St Andrew's church in Westland Row."
Mr McNamara said the concert is called Pride - In the Name of Love, but "this is purely a title taken from a U2 song to signify love", he said.
"It appears that they are happy for us to potentially perform once we don't align ourselves or be our real selves or show solidarity with our colleagues within the LGBT+ community," Mr McNamara said.
Mr McNamara said the venue, which is advertised as a concert venue, was booked in April and the choir's name was provided to the church.
That booking was then confirmed by email, he said, but on Tuesday they received an email from the church to say they could not hold the concert.
Mr McNamara said any issues or queries should have been raised in April.
In a statement, released to the Irish Times and The Irish Catholic, the church said: "St Andrew's Parish is happy to welcome groups from all backgrounds to perform concerts in the church.
"However, the parish is disappointed that the nature of this event was not made clear at the time of booking.
"We have learned that in form and content it is being presented not as a simple choral recital but as a Pride Festival event in a context which is not compatible with our mission as a Roman Catholic Parish Church.
"In the circumstances the parish is unable to facilitate the performance on June 23."
Irrespective of whether we are part of Pride, or not, it is either a concert venue or it is not, he said.
"They either are willing to accept groups of all denominations, of all backgrounds to perform within their facility as in a building or they are not," he said.
In December last year another LGBTQ+ choir performed in St Andrews, Mr McNamara added, and "we do not see how we differ from any other LGBTQ+ or community based choir".
"They're all songs based on the theme of love, humanity, family and togetherness," Mr McNamara said.
"And the whole concert was based on that principle."
Mr McNamara said there was "absolutely no intention" to provoke the church.
He said the choir has performed in Catholic churches but this is its first time to book a Catholic church as a venue.
The chorus has sold over 300 tickets, Mr McNamara said, and have secured a new venue at Sandford Church in Ranelagh for Sunday 23 June and all tickets will be valid for that.