I think in this case the Motte it self is indefensible in the end: RMS isn't the most charming guy and comes off as a creep: That's indeed not a persuasive argument, except, take into account that rather a large part of his job involves being a public advocate, and, well, either you teach the public not to get excited about someone who (literally, sometimes) puts his foot in his mouth, in which case, good luck to you, or, you sigh, complain about the tyranny of the masses... and fire him.

Is it fair? (And consider that I'm looking solely at the motte part; disregarding entirely this most recent event): Well, for most definitions of fair, it is not. Nevertheless, I don't think MIT, GNU, FSF, or any other entity should suffer significant damage just to chase the ideal of someone with RMS's peculiar ways gets to do the job of being an advocate of their organization.

It boils down to this: Is it acceptable to fire someone from a job based on something they are not really responsible for?

I think if the job description itself, prior to you taking it, makes clear that: Yes, you will be fired then – that it is fine.

The vast majority of clearly public facing jobs work like this. If you're the CEO and you do something rather upsetting, but not illegal, in a private setting that leaks out and which has absolutely no bearing whatsoever on the company or on your ability to perform your job there... you still get fired: The board weighs the value of your presence in your C-level role vs. the next best candidate vs. the damage done to 'the brand' by leaving you there, and a swift decision is made.

It's hard to draw lines in the sand on this. Both the public-ness of your role as well as the severity of how upset the public is about the unrelated thing need to be taken into account.

Imagine some sales rep at a company has a sextape leaked from years ago. Is it fair to fire them? Probably not.

Imagine that same sales rep has a penis tattoo'd on their forehead. Is it fair to fire them? Probably yeah, and the reason is not really: "They will do a bad job at sales itself". The reason is: "Most of your job is selling the product, put a small part of it is simply reflecting on the company. And with that tattoo you're doing such an incredibly bad job at that last part, we dont even want to know how well you will be doing at the first: You're out".

My point is, for RMS? I estimate that he is on the 'his firing his justified' side of the line for virtually anybody's sense of fairness.