Modern votes at the cash register often mean much more than those at the polling station, and the Olympics are no exception. When you take money away from someone, whether through loss of tourism or buyers in general, they are going to remedy the situation however they can to make back their losses. Boycotts are one of the most powerful means of change.
The 2008 Olympics are long over and the event went along without any serious boycotts. The 2008 Olympics in Beijing went ahead with near universal acclaim and commendation, and there were no serious boycotts or protests at the time, no should there have been - doing so only would deprive the athletes.