Judgment in the appeal by Ashers bakery over its refusal to bake a cake with a message supporting same-sex marriage will be given on Monday.
Directors at the business in Belfast are seeking to overturn a court judgment which found they acted unlawfully by rejecting an order placed by gay rights campaigner Gareth Lee in 2014 based on the religious conviction that the slogan was sinful.
The McArthur family, which runs the company, insisted they did not know the sexual orientation of the LGBT activist when declining his order.
Mr Lee had requested a cake depicting Sesame Street characters Bert and Ernie below the slogan 'Support Gay Marriage' for an event to mark International Day Against Homophobia. Bakery bosses refunded his money because the message went against their Christian faith.
The family insist their problem was with the cake, not the customer.
But Mr Lee claimed it made him feel a lesser person.
Last year Belfast County Court held that the bakery had discriminated against him on grounds of sexual orientation and religious belief or political opinion.
The firm was ordered to pay £500 compensation to the gay rights activist.
Mr Lee was also backed by the Equality Commission.
During the four-day hearing in May at the Court of Appeal, lawyers for the McArthurs challenged the finding by insisting it would have been sinful for them to complete the order.
David Scoffield QC who represented the McArthur family, said the person who took the order had no idea what Mr Lee's sexual orientation was and had never heard of Queer Space, which was part of the cake's message.
He said the alleged discrimination was not against Mr Lee, it was against the message, but the law only covered harm caused to an individual.
The commission's lawyer Robin Allen QC said the company directly discriminated against their customer. He said: "Mr Lee wanted to be associated with the class of person who have same sex orientation by purchasing this cake.
"He was not allowed to do that by the defendants.
"They would have allowed him to be associated with persons of opposite sex orientation by, for instance, letting him have a cake which did not have the word gay on it."