Bosses at the small family firm in Belfast are contesting an earlier ruling which said they broke the law by declining to decorate a cake with a pro-gay marriage campaign slogan.
The case against Ashers was taken by gay rights activist Gareth Lee in 2014.
Mr Lee had requested a cake depicting Sesame Street characters Bert and Ernie below the motto “Support Gay Marriage” for an event to mark International Day Against Homophobia.
The McArthur family, which owns and runs the bakery, refunded his money for the order because the message went against their Christian faith.
The family insist their problem was with the cake and not the customer.
But Mr Lee sued, claiming he was left feeling like a lesser person.
In May last year, a Belfast judge ruled the company had discriminated against Mr Lee on grounds of sexual orientation and religious belief or political opinion.
The firm was also ordered to pay £500 compensation to the complainant, whose legal action was backed by the Equality Commission.
The a case made headlines across the world and provoked intense debate.
At 10am on Monday, the Court of Appeal in Belfast will deliver its ruling on the controversial case.
Peter Lynas, former barrister and Evangelical Alliance NI director claimed Ashers had discriminated against an idea, not a person.
He added: “While the law rightly prohibits the later, the former is not only allowed, but encouraged in a healthy democratic society.
“A law designed to protect a minority is now being used by the new majority to force their views on others.
“What began as a battle to remove state discrimination against the LGBT community, now seeks to use state power to punish those who refuse to support same-sex marriage.
“If this appeal is lost, freedom of conscience and religion will effectively be banished from the public square for everyone in Northern Ireland. This is not about special protection for Christians.
“The mark of a democratic society is that competing views are discussed and debated. Forcing someone to promote a view that they fundamentally disagree with is the antithesis of a free and fair society. Let’s hope justice is done.”