Going to pass over details such as violent fanatics, personal opinions, and the other nonsense... but one of the biggest dangers of social networking, of which professionals are aware of (but let's assume the fired employee was not, likely because he wasn't a licensed professional and hasn't got the memo), is how easily you can ruin your own reputation through it. Here's some of the general guidelines:
#1 - If you can, avoid using social networking.
Perhaps overly strict, but the safest way to avoid images of you doing something which could harm your reputation as a professional getting posted on Facebook... is to simply not have an account on Facebook. While not an absolute guarantee, things won't be so readily linked to you having a bit too much fun. Not being a really social person myself, I haven't started using any of the social networking sites; I also have no intention of starting to either, I don't need it and there's no point for me to invite this risk.
#2 - If you are using social networking, don't use your real name.
The most common way this is done is to use your first and middle names, forgoing your surname. Avoiding professional titles wouldn't be a bad idea either. This allows you to keep some distance from your online persona, and to keep people from your professional activities out of your personal life. Even though I try to keep a decent of conduct online, I always use an alias; this is just good practice to keep yourself out of any accidental trouble because you couldn't control yourself online (which seems to be a very common occurrence).
#3 - Use whatever controls you can on social networking to limit such images being posted or linked to you.
Only something I've heard of (again, don't use Facebook or anything like it myself), but it can be set so that an image can't be linked to you unless you personally approve it. Again, just keeping yourself out of trouble by any means necessary.
#4 - If you are using social networking and your real name on it, be very careful of what you say and do.
In the event there's no way you can avoid dissociating your personal and online activities from what you do in profession, the utmost level of control must be taken. Reputations, once brought down, are notoriously difficult to rebuild. It's easier to get from being an unknown person to being regarded as one held in high esteem than it is to cast off a negative reputation (let alone reclaim any measure of prestige). Saying something stupid and offensive, opinion or otherwise, is the fastest and easiest way to get expelled from anything.
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The Eidos employee wasn't just fired because of his actions, he's probably been black-listed. I'm not just saying he's not going to have a great deal of difficulty finding a job in the games industry again, he's going to have trouble finding it anywhere. No one is going to want to hire someone who said what he said, to safeguard their own reputations. In fact, that's pretty much the reason he was fired; Eidos doesn't want to be associated with anyone who said that, period.
I actually pity him, because he's got an exceptionally rough road ahead in his life. He didn't just make a small mistake with his statements, he made a huge one; and it will be an eternal albatross around his neck. Any future employers are always going to be watching him, how he acts and what he says; he's going to have to be very careful with what he does, period.
I would actually wish him luck, he will be needing it.