I think it comes down to evaluating the strength of one's beliefs and the relative importance of what one is about to say. Lets face it, publicly expressing an opinion has consequences, especially if that opinion covers an area about which other people feel passionately. Thanks to the internet, that's pretty much everything. There's a real cost/benefit analysis that can, and should, go into public criticism. Having said that, anyone who puts their opinions or work out into the public sphere shouldn't cry victim if their audience responds, since the whole purpose of the endeavor was to provoke a response. Presumably a positive one, but that's the risk we take. Cruelty certainly isn't acceptable, but I've no sympathy for people that react badly to legitimate, measured criticism of the work they asked us to pay for and spend our time reading.
My personal criteria for self-censorship is whether or not I feel a discussion or potential conflict has value. If not, I'll generally play nice, since I see no merit in engaging in mindless conflict for it's own sake (can we say youtube comments?). That calculus changes, of course, if the pointless conflict is rooted in something deeper that I do very much care about. When it comes to issues that are important to me, so long as I'm willing to take the proverbial heat, I do my best not to self-censor, and I encourage other people not to either. If I choose to plant my flag on an issue, I better be conscious and willing to defend it without whining about 'censorship' or 'persecution' just because other people disagree with my position.
In the specific case of authors/artists and social media, it seems to me that the basic fear is that economic concerns (don't offend potential readers/clients) will trump artistic ones, to the point where nobody has any opinions about anything substantive and nothing interesting gets written or discussed. At least that was my take-away from the Guardian bit. That's probably a reasonable risk, to an extent, but then again, how much do I really want to read something written for purely commercial reasons, by an author all too willing to subvert their own point of view in an attempt to please everyone on the internet. If anything, I imagine a trend towards excessive self-censorship will only make the impassioned writers and critics stand out, which will save me time.
With respect to 'binary' discussions, that kind of language always smacks of post-modernism. It's probably a bias I have, as it's a huge pet peeve. On subjective issues like artistic merit, sure, there's a million opinions and there's no reason to form rigid camps. On other issues there is either a reality-based or non-reality based position, and there shouldn't be any room for compromise. I realize I'm going a bit far afield with this example, but as an infectious disease specialist, I'm occasionally driven to conniption fits by the dangerous mis-information and ignorant opinions that get flung around the internets on various health topics. Vaccine denialism is a big one (thanks Andrew Wakefield and Jenny McCarthy, thanks a bunch
), and in those sorts of discussions I absolutely don't self-censor, nor do I consider a lack of compromise to be a bad thing. I'm (usually) not rude, but I don't shy away from explicitly stating that somebody else's belief is utterly wrong, dangerous, and logically incoherent.
Drifting back to the realm of books and authors and such, the first name that popped into my head when I read that link was: Christopher Hitchens. Not a surprise. I have no doubt that the man censored himself extensively, but he certainly didn't shy away from offering a controversial opinion on anything. I think the take-home from him was that if you are going to go wading into the muck, be clear, be coherent, and be fearless. Nothing destroys the integrity of a discussion faster than half-expressed opinions, waffling, and the dance of political correctness. The same is true of art. While you can't really win on the internet, I do believe that offering an uncensored but cogent position on a subject is often of greatest benefit to the readers, not necessarily the other commenters (and certainly not the trolls).
In a debate, you might have 1 opponent but 500 audience members. Who are you really trying to reach? The signal-to-noise ratio on the internet may be unfavorable, but that only reinforces the need to be clear, thoughtful, and at times quite forceful on any subject that matters.
Hrm. Apparently today is manifesto day. Ah well, I stand by it.