What if the couple was black? And, the baker was a white supremacist who sincerely believes that the Bible condemns the black race
To decide if that should or shouldn't be allowed, simply reverse it - if the white guy wanted a cake decorate with the Confederate flag and the black baker didn't want to make one, should they be compelled?
The best, sanest thing is to allow anyone to refuse any service as long as it's custom. What you can't do is refuse to sell someone something that you are willing to sell to others simply because you don't like some identifiable trait. So, you can refuse to bake and decorate a cake to someone's specification but you can't refuse to sell them a pre-made cake that is on sale in your store.
However, you can have other rules which can be imposed on customers on your premises which may be todo with dress (shirts must be worn) or other attire (no helmets / face-masks). Again, as long as they are applied equally and to all.
The only time someone should be compelled by the government to provide service is when that service is meant to be provided by the government. So, the religiot that was refusing to issue gay marriage licenses should lose her job and be marched out because that is her job to do that and if she doesn't find her conscious allows her to do that she should find another job.
But even then, the employer should find alternative employment in the same way that a Muslim stewardess refusing to serve alcohol on a flight would be allowed to keep her job. If the private company would be prosecuted for firing someone who won't / can't do their job, then the government should have the same standards applied to it.