The tone of a passage of text is part of the meaning that it conveys. That's about the first thing you learn in English 101, and it's the reason why tone is important. As a one-time English lit. teacher, I wince every time I see the suggestion - usually from commenters in the blogosphere, not so much in actual blog posts - that tone just doesn't matter. It really does.
One of the things that people coming to university straight from high school have usually not picked up is the whole concept of tone, although it's not actually that difficult. It's analogous to the tone of voice that you adopt in oral communication, which conveys not just a lot of affective content, i.e. the emotions you are feeling, but also your attitude to the listener. Your tone may be conspiratorial, inviting the listener to plot and plan with you. It may suggest that the listener treat what you are saying as a joke, or as irony or sarcasm. It may communicate anger at the listener, or it may invite her to share your anger with a third party. It may suggest that you hold your listeners in contempt, or that you respect them (even if you are disagreeing about something). It may express amusement or exultation, and invite a friend to join in. And so on. It's a very important part of communication.
In face-to-face communication, much of this is conveyed by literal tone of voice - which can be cashed out more reductively in terms such as volume, pitch, pacing, intonation and emphasis, and the like. Some of it is conveyed by facial expressions, another part by gestures/body language. All these combine to carry much information to the hearer about how you regard him or her, how you want your words to be taken, how you are encouraging him or her to feel or act. In many circumstances, this might even be more important than the literal words, as they would appear if transcribed (if I am speaking to someone I love, the most important message of all for her to understand may well be that I'm speaking to her lovingly).
Of course, literal tone of voice, facial expressions, and gestures/body language are all missing in written communications. However, skilled users of the language (whichever language it is) are able to convey much the same information through register, vocabulary, prose rhythms, and style. Skilled readers are able to use these cues to pick up the information, some of which may be quite subtle (sometimes so subtle that two equally skilled readers may disagree as to what actually is being conveyed ... and sometimes that's because of deliberate ambiguity on the part of the writer).
Unfortunately, some writers and some readers are much more skilled at this than others. In a standard English literature course, you will invariably encounter writers who are masters at it. But students are not always masters - if you actually teach literature, press for detailed responses to a passage of prose or verse, and maybe mark essays, you'll discover that a lot of otherwise-intelligent people are not all that good at picking up on the tone even of relatively simple texts, especially if these are from earlier historical eras. Talking about these aspects intelligently is not easy at all; and most people, when they can, avoid saying anything too detailed.
Much of what goes on in a university Eng. lit. course is all about reading complex texts, trying to develop some sensitivity to the less literal apects of what they convey, and learning to write about this intelligently, and to debate it. (Lit. students please take note.) There are real skills to be learned here, and I bristle at the notion that it's all bullshit, or that this kind of literary training imparts nothing of substance. It imparts a great deal of knowledge, and it opens up capacities for understanding and enjoyment of our heritage of drama, poetry, and prose narrative. Not to mention a heightened sensitivity to elements of everyday communication.
So, forgive me when I'm unamused each time that I read something about how tone is unimportant, or that comments about tone are ipso facto beside the point, or that they're some kind of mumbo jumbo. Some kind of fraud. That's not the case at all.
Of course, there may well be a sense in which, in a particular context, tone does not matter. If I offer a formal argument for some proposition, complete with premises and conclusion, it doesn't matter if I adopt language (or, in a face-to-face discussion, provide other cues) that suggests I think you're a fool. No, that's wrong. It does matter, perhaps in more than one respect, that I'm conveying information about what I think of you ... but it doesn't matter in this respect: It Doesn't Affect The Cogency Of My Argument.
If someone complains about the tone of one of my posts, I am entitled to respond that this goes nowhere towards showing that any argument in my post lacks cogency, or that any conclusion I've drawn is false. And yet, I took the tone that I did for a reason. My choice of vocabulary, my prose rhythms, and so on - all the elements that add up to "tone" - are conveying something important about how I feel about my readers, how I'm inviting them to think or feel about others (or themselves) and so on. The tone I chose to adopt will have consequences: some people may be amused, others may be hurt; the general tone of a larger cultural conversation in which I'm involved will be affected to some degree, perhaps making it easier for people to get along, perhaps making it harder; particular third parties may be affected if I've managed to insinuate certain attitudes towards them.
The tone that people take with each other, and their perceptions of tone, are not trivial. They can make or break relationships.
For these sorts of reasons, intelligent discussion of tone is always in order. The problem is likely to be that a lot of discussion of tone is just not very intelligent - how many reviews of The God Delusion have you read that show a tin ear for Dawkins' control of tone? Many reviews don't show any sensitivity at all for the varied tones: the humour; the quiet thoughtfulness and introspection; or the comical intoxication with language itself in Dawkins' famous denunciation of the Old Testament deity. Generally speaking, the reviewers just don't "get" it. But the cure for that isn't less discussion of Dawkins' tone; it's more intelligent discussion of Dawkins' tone. A hackneyed adjective such as "strident" doesn't cut the mustard.
To say that intelligent discussion of tone is always in order is not to accept that the tone of political, scientific, or philosophical discussion should always be calm and respectful. There's plenty of room for passion, mockery, and outright denunciation. Not all the time, perhaps, but in their place. Some things deserve to be denounced or mocked, and sometimes it's necessary to use these elements of language to bring home the essential implausibility or even absurdity of a position. Someone who can adjust forever to logical arguments, in the process moving to a wildly implausible but internally consistent position - may well be shaken into seeing how the whole thing looks from the outside.
Complaints about tone can be misguided, as in this link, and they sometimes seem like attempts to evade other matters to do with the cogency of arguments or the correctness (or plausibility) of conclusions. But again, discussions of tone should not written off as automatically illegitimate or intellectually bogus. Rather, the point is to insist that discussions of tone be intelligent and that judgments about tone be relevant to matters at hand.
If, for example, you think the widespread adoption of a particular kind of tone - say, a denunciatory or mocking tone - is poisoning debate ... well, you need to show that this tone really is widespread, you need to be able to define the tone of your examples with some precision, you need to show the links between them that you claim to see, and perhaps much else. And you need to put your own plausible argument about why the effects you foresee will occur, as opposed to the effects that the writers concerned may have in mind.
Tone matters, but dumb complaints about tone are, as they say, Not Helping. They don't make progress.
If you want to talk about tone, go ahead, but try to say something intelligent about it.