Unless I've seriously misunderstood this, I think that they did refuse to perform the service.
//His order was initially accepted at a branch of Ashers in Belfast city centre, but two days later the baking firm's head office contacted Mr Lee to say the firm would not make the cake.//
I understand the free speech argument about the slogan, but I don't find it very convincing. The only possible reason that they could think the slogan is inconsistent with their faith is if they think being gay is wrong.