The case involving Ashers bakery in Belfast, which refused to decorate a cake with a pro-same-sex marriage wording has now been referred to the European Court of Human Rights (ECHR).
Ashers was found guilty of discrimination in 2015 for refusing to make a cake for Gareth Lee. This ruling was overturned by the British Supreme Court in 2018.
The bakery’s Christian owners refused to ice the cake because of their belief that marriage should be between a man and a woman.
However, they said that their objection was to the slogan rather than to the customer Gareth Lee.
The ECHR appeal will argue that the British Supreme Court "failed to give appropriate weight" to Gareth Lee’s rights under the European Convention of Human Rights.
Lee’s lawyer Ciaran Moynagh said: "The Supreme Court judgement... creates the risk that some people may fear going into certain shops."
Mr Moynagh added that this is "a dangerous position for minority groups and vulnerable people..."
Long-standing gay rights campaigner Peter Tatchell backed the bakers saying: "Ashers did not refuse to serve a gay customer, which would have been wrong and rightly illegal.
"What they did was decline to put a 'support gay marriage' message on a cake.
"Equally, I don't believe a gay baker should be compelled to decorate a cake opposing gay marriage."