Boycott Chinese businesses! Boycott countries with sweat shops! Don't eat at this restaurant because their political views aren't what I think they should be! Don't eat this or that because I don't!
The truth is that when a nation imposes economic sanctions on another nation, only the poor are hurt. Rulers continue their same opulent lifestyle despite sanctions. Remember the years of economic sanctions on Iraq? Saddam Hussein didn't sell his palace to cut corners, he just made sure even less flowed to the average citizen. Similarly, Fidel Castro didn't go without during all the years of the U.S. trade embargo. Similarly, when we decide as a nation not to send medicine to other nations as some kind of punishment, the leader still gets antibiotics - but the poor people donxt.
The same is true of individual decisions we make. I fully support a free Tibet, but I recognize that it isn't going to happen because people decide not to buy Chinese goods (even if it was possible). I say that because Chinese leadership would not be effected by such a move, no matter how successful it was.
Here's the kicker: the fact the Chick-fil-a isn't on board with LGBT issues is (in America at least) within their rights. If I decide not to eat there because of that (and I don't eat there), I need to be aware that the person I am hurting the most is the minimum wage worker who, no matter how many showers she takes, smells like chicken. Why? That minimum wage worker who can't look a piece of chicken in the beak will be the first to lose her job. How many of those people will have to get hurt before the CEO feels an impact? I'm afraid a lot of them will become unemployed before the shareholders feel a pinch.
I'm not saying boycotts are always wrong. Boycotting Rush Limbaugh and similar idiots doesn't cause a lot of collateral damage. What I am saying is that we all need to make our own decisions to participate in boycotts or support economic sanctions. Choosing to opt out doesn't mean we don't care about the issues. It means that we have evaluated the broader impact of the suggested action and decided the ends don't justify the means in that particular case.
Many if not most of us are far too eager to attempt to compel others to do things rather than take the time needed to convince them to do the same things. Force is alnost always faster, but it tends not to have a lasting effect and to create enemies in its wake. That more than offsets the gains made.