When constitutional rights duel, which one wins?

A gay couple walks into a Christian deli/bakery in Texas wanting to order a wedding cake and associated catering services, and the owners refuse on the basis that their strongly held religious beliefs consider homosexuality an abomination and thus forbid their participation.  What's likely to happen next?  We all know that the local media, tipped off by gay activists who were just waiting for the expected response, will immediately pick up on the story and present it as another example of homophobia and discrimination against members of the gay community.  The local lead will be grabbed by the national liberal media and whipped into a froth of indignation, setting the scene for a federal discrimination lawsuit based on violations of the gay couple's constitutional right to equal treatment as American citizens.

At the same time as that gay couple walks into the bakery, just a couple of doors down the street, a medically retired sergeant first class, an Army infantryman with a Purple Heart earned for the loss of his lower right leg during the last of his multiple combat tours in the Middle East, walks into a national coffee chain with his son and orders two large black coffees, no cream, no sugar, no nothing but coffee.  The barista notices the .45-caliber semi-automatic pistol holstered on the sergeant's hip and tells him he must leave, as no firearms are permitted on the premises, as a sign by the entrance clearly explains.  The sergeant apologizes for failing to notice the sign, and he limps out quietly, followed by his bewildered young son.  No gun rights protesters are waiting outside to begin a loud demonstration, no local TV station has been alerted, and there most certainly will be no high-publicity lawsuits filed.

The bakery owner feels that the freedom to practice his religion without government interference allows him the freedom to deny his services to the gay couple who feel they are being deprived of their right to equal treatment under the law.  The retired soldier is exercising his clearly stated constitutional right to keep and bear arms.  The coffee corporation is enforcing a corporate policy allowed under Texas law, but less constitutionally certain, to ban the presence of firearms on its premises, a right fortified by a long tradition of property rights.

Conflicting rights in both cases – yet in only one will one side be taken by the media and used to portray the other as a shameless bigot and denier of constitutionally guaranteed protections, bringing the obvious question:

If not for the determined gay activists and a complicit media, is there any real difference in terms of our constitutional rights?  Does the biblically inspired local baker have a lesser right to conduct his business as he sees fit than the corporate coffee sellers who impose their policies based on a liberal corporate culture reflective of the CEO's personal bias against firearms?  What would be the result if the baker put a sign in his window politely explaining that his religious beliefs prevent him from participating in gay marriage ceremonies?  Is that at all different from the corporate coffee shop saying that you must suspend your constitutional right to keep and bear arms to enter these premises because our owner dislikes guns?

You tell me...