You know that it was the group, and I know it was the group. But it’s still a product issue. The business gets to decide what they will print and what they won’t print — as long as their list of what they won’t print applies to everyone. If they refuse to print this design, that’s their right, as long as they refuse it for everyone. Furthermore, if they say they won’t print something, and apply that to anyone, their reason is immaterial. They can refuse for any reason.
If they printed a particular design or text for straight people, but denied the same design or text to gay people, that would be discrimination, and illegal.
However, even though they have the right to print or refuse to print whatever they want — as long as they print or refuse to print a particular design or text to all customers — the general public can certainly publicize their refusal. Yelp reviews, social media, etc. — gay people aren’t the only ones whose business this shop would be losing. There are a lot of straight people out there who object to doing business with bigots, regardless of how “religious” they are.