I don't like the extremism behind the idea that we should fire someone from their job over a off-color joke which is intended for a small audience, but may be overheard accidentally by others.
That sort of absolutism of policing thought just doesn't end well, ever.
To translate it away from Twitter: imagine you're at a public space, such as a mall, and you happen to be walking by a table of people leaning together just as one makes a racist joke.
Is your response a) give them a sort of disgusted look and go on about your day or b) call everyone you know and repeat the joke to them, along with the location of the table in hopes you can whip up a mob of people to shout obscenities at them, continuing to follow them around for the day, and eventually form a mob outside of their office building, continuing to shout at them until their employer fires them?
Most of us would go with 'a' and not 'b', because we realize that what happened doesn't really fit the extreme response. It's interesting to me that people feel that more extreme response is okay, as long as they don't feel personally too involved with it (eg, they can shout remotely).