"So here's a question for you, and really just to dig deeper on this, I'm not trying to trap you: what about those southern barbershops with the "Whites only" signs in the '50's? Do the owners have the right to refuse service based on race? "
This is a tricky one. I think, at the time, they had every right. But as color is not something that can be hidden (don't ask don't tell comes to mind), it is a more black and white (no pun intended) issue and is more problematic because it is so obvious as to encourage more recriminations against blacks. I don't think a store should ever put up a sign that says "We refuse to serve homosexuals." But the real question is, should they be allowed to refuse service to other races? I would say no and read all of this...
I say that because race isn't a choice at all. There is still debate if sexuality is or not. Nature versus nurture. Race is clearly 100% nature. Same as traditional gender (M/F, not including the transgendered for now). But sexual orientation is potentially nurture and religion is often the same. So, if someone is allowed to say "We don't serve Satanists or KKK groups" they should also be allowed to say "We don't serve LGBTQ".
Now, I want it clear that I don't believe any non-traditional sexual role is bad at all (except rape, child abuse or animal abuse). But I understand the point of view of the extreme religious individual, especially the case of a photography studio whose owner and employee would have to attend the wedding. He should have the right to refuse any situation that would make him feel uncomfortable. A wiccan wedding, a Satanist wedding, a nudist wedding, a gay wedding. Doesn't matter. Likewise, if the product he is creating (the baker and the t-shirt company) is distinctly offensive to his sensibilities, he should have the right to refuse to make it. Now, if they came in and ordered a traditional wedding cake with nothing distinctly "gay" or "satanic" or "wiccan" or "nudist" about it, then no, he shouldn't be allowed to say no. But then the person ordering the cake need not mention it is for a gay/satanic/wiccan/nudist wedding to get it made. Same with the t-shirts.
On other services, like the transport of goods. There are plenty of transportation companies out there, so refusing to transport a product the owner finds unsavory should be completely within his rights.