An employee of a British mobile phone company was suspended last year for publishing a joke about Islamophobia. With the London transit bombings in mind, he defined it as the fear that your bus might explode on the way to work.
I think it was a witty comment on a big issue in modern travel: that it's not the sign of a phobia or bigotry to be concerned about terrorist attacks.
But let's say that he swore like a trooper on his site. That would probably have had him suspended as well. And if he had actually encouraged bigoted ideas and hateful feelings, there would be no question about his fate.
And, indeed, if people refuse to do business with your company because of the content of an employee's personal blog, you'd have to be crazy not to can the employee or force him to hide his identity when he blogs.
But the courts might not agree. I'm pretty sure that it's not legal in most modern countries to dismiss an employee because your customers object to her gender, sexual orientation, race, creed or colour. So, how can an employee be denied her right to blog his mind even when customers don't want to buy from a company that employs people like her.
Papa John Sumser is publishing a series on Employee Blogging