Let's take a sequence of events: Somebody is Wrong on the internet. And not just Wrong about, you know, gun control or abortion or whether to vote Democrat or Republican (or whether the rest of the world outside the USA actually exists as anything more than a fable or source of rhetorical ammunition) but displaying bigotry against some minority group. Because the internet is inherently a public medium, people who belong to the minority group are going to notice, and are quite likely to express their hurt feelings. What happens now?
People don't like being criticized in public, especially when it's something that touches an important part of their self-image. A bigot is a bad person in most people's understanding these days, so it's hard to hear "this action or comment has bigotry-promoting consequences" without hearing "you're an evil bigot!" So the accused person is very likely to get defensive. In scrabbling to find reasons why the accusation can't possibly be true (because I'm a good person!), they're likely to cause more harm. For example, they may accuse the minority group of being over-sensitive or stupid, or claim that bigotry is a thing of the past. If the targeted minority was hurt before, being called stupid or told that their experiences of discrimination don't really matter to real people is likely to make them incensed. Because the internet is the internet, they'll deal with this by complaining to all their friends. The friends will rush to support the target and try to make the originally accused person see reason. Inevitably, the accused person will also get support from their friends, and the more tempers run high the more random second-degree connections and eventually total strangers will start following links and everything will get amplified and messy. (I very much like cartesiandaemon's comment on outrage:
if I'm a little bit outraged, it might either look like (a) I think amazon were only a little bit culpable or (b) I only care about discrimination a little bit.)
Once things get horrible in public, people who don't really know the original facts will conclude that the whole thing's just a pointless flamewar, and that both sides are equally at fault. The people who are complaining about bigotry get accused of dogpiling, of ganging up, of being too angry and aggressive. And because emotions are already running high, you hear the rhetoric of violence, talking about mobs or lynching or angry hordes.
I think what really drove this home to me is that some people are taking this line regarding the AmazonFail story; the people who twittered about it and got large groups of people shouting about how Amazon is homophobic and they're going to stop buying from Amazon until there's a proper apology are being classified as an angry mob, getting carried away by the crowd dynamics, rushing too quickly to violence before they know all the facts... Waitaminute! Deciding to buy books from Barnes and Noble instead of Amazon because you don't like Amazon's homophobic policies is not violence. It's not even a little tiny bit like violence. Googlebombing is not bombing. A commercial boycott is neither social shunning nor, most certainly not, declaring war! And this is Amazon, this isn't even an individual person who meant well but said the wrong thing in an internet discussion and ended up getting their feelings hurt and understandably their friends want to take their side.
Part of it is an instinct to go against whatever the crowd is doing; if everybody is angry with Amazon, it's natural to want to defend Amazon, to feel like a balanced person who sees both sides of the argument. But realistically, Amazon is not the underdog here. Straight, gender normative, able bodied individuals are not the underdog here. (Some of the worst of this is in the Making Light post on the subject, and again understandably, the mods are not very happy about the comparison to RaceFail. Which is why I'm taking this here rather than trying to comment in that thread.)
The other thing I want to talk about is the asymmetry. On a very crude level, it means something different when a white person calls a black person stupid, from when a black person calls a white person stupid. A white-only club is a very different thing from a club for an ethnic minority group to get together and provide mutual support. But there's another aspect to this. There are some techniques which the powerful use against outsiders, such as shunning and social exclusion, such as getting a big group together to gang up on one individual, such as shouting and aggressive mannerisms, and so on. That's definitely bullying, and since many people who make their social life on the internet were bullied as kids they're very sensitive to it. But when a group of hurt people get together and decide that they don't want to socialize with someone who keeps hurting them, that's not the same as social exclusion. When people get support from their friends in order to defend themselves against bigotry, that's not the same as ganging up or piling on. When a member of a minority gets angry about being constantly mistreated based on a superficial characteristic, that's not the same as a powerful person yelling at someone in a subservient position in order to intimidate them. Refusing to do business with someone because you don't like their skin colour is not the same kind of action as refusing to give your money to a business that discriminates.
Equally, some of the dynamic I'm seeing is that people with power are adopting some of the tactics used by discriminated groups to try to lessen discrimination. For example, suing institutions for discrimination against white people or men if they have policies to try to support POC or women. Accusing people of intolerance when they complain about bigotry. Again, complaining about homophobes is not at all equivalent to discriminating against gay people!
There's another aspect which is a bit harder to define. Often, part of unconscious prejudice against minority groups is that the same reaction is perceived as being more aggressive than coming from a higher status person. This is partly because of direct stereotypes about the group (eg "black people are violent and animalistic"), and partly because groups that experience discrimination often learn to be extremely polite, deferential and conciliating and any deviation from that is perceived as threatening (eg a woman who complains about sexism instead of trying to adapt to it is "a man-hating feminazi"). It's also partly because people are quite naturally more inclined to give the benefit of the doubt to people like them, and if people like you happen to run society, then they get a whole bunch of automatic credibility on top of that. Also, it's a big problem when a group that is generally not subjected to violence uses the rhetoric of violence to dismiss the complaints of a group who do fear actual, literal violence.
In the probably vain hope of forestalling annoying responses to this, I want to point out that I am NOT saying that anything that a person from a discriminated background ever does is right, or that anyone who shares characteristics with the people who generally wield social power is automatically in the wrong. I'm saying that I've seen a lot of dynamics where an argument between powerful people who are behaving in a bigoted way, and vulnerable people who are complaining about that bigotry is perceived as "both sides are just as bad as eachother". Or when both sides do in fact behave badly, the less than perfect behaviour of one or two representatives of the minority is treated much more seriously than all the bigotry which led to the situation in the first place.
In conclusion: calling someone a homophobe is really not equivalent to calling someone a f*ggot. Calling someone a racist is really not equivalent to using a racial slur.