From a purely philosophical standpoint, I can see, and largely agree with AJ's point. However Starbucks, as a publicly traded business, has to look at what's best for their shareholders. I don't know if their current position does that, but I can see their management figuring 'appeasement" and "lets hope this goes away" as the best course to keep the stock from dropping.
I don't necessarily like using something that's not a right and that some would consider a vice as part of my analogy, but I liken the "guns / no guns" issue at Starbucks to "smoking / no smoking". There is no doubt the antis started the hullabaloo, by sticking their noses into the business of a few people open carrying in a Starbucks. Then the gun community got wind of it, and the next thing you know, you have far above the statistical average of open carriers at various Starbucks, not just open carrying, but vocalizing that they are. Now you have people at the Starbucks who didn't care about the few people a day coming through with guns who don't necessarily feel comfortable with a "mob" of open carriers who are there not for a cup of coffee, but to prove a point.
Just like with "no smoking" bans. If a place (bar, restaurant, whatever) has one or two smokers, maybe most people don't care. If an anti-smoker complains though, and the next thing you know there are fifty smokers in the place, not to specifically partake in whatever the place offers, but to prove they have the right to smoke, you now have patrons that didn't care, or were only slightly bothered before, complaining about all the smoke in the room. If the business thinks it will get more business from smokers than from non-smokers, it may ignore the complainers. If it thinks it's now going to lose business, because all those smokers are only there to prove a point and they won't be coming back, it may be more likely, from a purely business standpoint, to put up a 'no smoking" sign.