The bakery, named after a verse from the Bible, is based in Northern Ireland, the only part of the UK where same-sex marriage is not legal.
General manager Daniel McArthur said: “I would like the outcome of this to be that any Christians running a business could be allowed to follow their Christian beliefs and principles in the day-to-day running of the business and that they are allowed to make decisions based on that.”
Gay marriage is a highly divisive issue in Northern Ireland and while the bakery’s decision has been backed by Christian advocacy groups it faced criticism from gay rights organisations which argue that discrimination in delivering services is illegal.
The devolved assembly at Stormont has rejected several attempts to change the law on gay marriage and local politicians have intervened on both sides of the bakery debate.
Ashers was founded in Newtownabbey, north of Belfast, in 1992 and is run by the McArthur family. The Christian directors oversee six shops in Northern Ireland and employ 62 people.
The company was named after a verse from the Bible, which refers to “Bread from Asher”.
Mr McArthur, 24, said the customer placed the order at the Belfast branch a number of weeks ago and it was considered by company head office, which decided it was at odds with the organisation’s beliefs.
He said: “It certainly was in contradiction with what the Bible teaches and on the following Monday we rang up the customer to let him know that we could not take his order.”
The firm gave a full refund but six weeks later received a letter from the Equality Commission, which helps those who complain of discrimination.