As the Facebook “dirty coal” protest builds steam, we take a look at the thorny question: when should a company, in the face of revolt, change course and give in to the demands of the public, and when should they merely watch from the sidelines?

To be sure, this is one of just thousands of ongoing protests and boycotts of major brands, both big and small, circulating today on Twitter, Facebook and on blogs. When the public grows restless online, big brands have two simple choices: do nothing and hope it blows over or intervene. As social networking grows more influential, the latter course of action will occur much more frequently.

Here then are some examples from the past when companies decided to act and why:

Risk of alienating a core customer group: In 2007 recent graduates in the UK came together on Facebook to protest HSBC’s overdraft charges policy. Why? Smartly, the company did not want to risk alienating an important segment of its customer base, one whose earning potential is just about to mature.

Risk of punishing regulation: Goolge and Facebook share the stage here. Privacy advocates have taken Facebook and Google to task for introducing, respectively, Beacon and Google Buzz, following howls of protest from users. Caving to users’ demands here is always less painful than a dose of medicine from regulators.

Risk of a tarnished brand image: A classic example occurred in 2008, when the foremost British technologist Tim Berners-Lee took to task Phorm, a creepy adware technology backed by, among others, Britain’s most visible technology company, BT. If the father of the World Wide Web is against it how can any well-meaning technology company risk crossing him? BT and others walked away from Phorm and their reputation among geeks was preserved.

In the case of the green backlash now facing Facebook, the company faces two of the three big decisions above: when to jump in to avert alienating a core user group and when to step in to preserve its brand reputation?

It also calls into question a larger issue for Facebook. Its de-facto corporate motto “Move fast and break things,” may have served it well in the early days, but eventually Facebook will need to define what – if anything – it stands for. Otherwise, it will be facing accusers on a regular basis.