To be quite honest, while I understand the sign was meant more to make a statement than as an enforced rule, it can very easily come across as bigoted itself. Racism's generally pretty cut-and-dried, but what qualifies as "sexist" and "homophobic" is vague at best, and in my personal experience (which I understand doesn't necessarily reflect on the entire pro-LGBT or feminist community) most of the people who accuse others of being sexist or homophobic primarily make such accusations of anyone whose opinion they find the least bit unpleasant to them personally. To use two purely made-up and admittedly extreme examples,
1. Jim gets accused of being sexist when he says he thinks men and women, though equal in value, are general better suited to different things.
2. Sally gets accused of being homophobic when she calmly points to passages in the Bible that make it clear that the Bible regards homosexual intercourse as sinful.
These are not uncommon notions of what is meant by "sexist" and "homophobic," as they're often used more as insults than legitimate accusations. So the message the sign sends to people who don't support gay marriage or who do believe men and women are different (whether the shopkeeper intended this message or not) is, "You have an opinion that is different than mine, so you're an asshole and I don't want your business." It's not somehow less bigoted when it's the majority opinion that's doing it.
Of course, I also realize that message may not have been the shopkeeper's intent, but in that case, the sign is merely rude and inconsiderate. Sure, it may have come about because of someone else's rudeness and inconsiderateness, but I've personally never felt that rudeness justifies rudeness.