Say they didn't want to support a mixed race marriage? Would you be fine with that?
Two issues with claiming that if it's ok for a black person to marry a white person then it's ok for a man to marry a man:
1. A race is a group of people of common descent. Therefore: a. Black and white people are of the same race, and b. If you want to base the argument on them being different sub-races, you have to accept that all marriages are between people of different sub-races (according to the definition above), so if mixed race marriages were disallowed, by extension why not ban all non-incestuous ones?
2. It isn't the characteristic of same sex attraction, which can be compared with skin colour, that is the problem, but the action associated with it, which cannot.
A trader might believe that same-sex sex is forbidden by God, since God intended sex to be between a man and a woman. Or he might, in his own reasoning, believe that it is an unnatural form of sexual activity, and be unwilling to become involved. Provided there are other florists (or whoever) available who are willing to provide the service, I don't see any harm in a 'conscientious objector' referring a same sex couple to another florist who is. I don't believe that penalizing such an objector is fair, provided they don't act in a way that is in any way hateful.
You might ask: if we are basing the rules on actions, and we say that if a man is not allowed to have sex with another man, then why allow a black man to move to a high latitude? Well if a black person living in Scotland finds he isn't able to get enough Vitamin D, he still has the option to move to a lower latitude.
The marriage vow, however, is inherently a lifelong commitment.
So I think people can justifiably refuse a service if it involves participation in same-sex marriage.