Suppose, for a moment, you're a strong proponent of Glim, a fantastic new philosophy of ethics that will maximize truth, happiness, and all things good, just as soon as 51% of the population accepts it as the true way; once it has achieved majority status, careful models in game theory show that Glim proponents will be significantly more prosperous and happy than non-proponents (although everybody will benefit on average, according to its models), and it will take over.
Glim has stalled, however; it's stuck at 49% belief, and a new countermovement, antiGlim, has arisen, claiming that Glim is a corrupt moral system with fatal flaws which will destroy the country if it has its way. Belief is starting to creep down, and those who accepted the ideas as plausible but weren't ready to commit are starting to turn away from the movement.
In response, a senior researcher of Glim ethics has written a scathing condemnation of antiGlim as unpatriotic, evil, and determined to keep the populace in a state of perpetual misery to support its own hegemony. He vehemently denies that there are any flaws in the moral system, and refuses to entertain antiGlim in a public debate.
In response to this, belief creeps slightly up, but acceptance goes into a freefall.
You immediately ascertain that the negativity was worse for the movement than the criticisms; you write a response, and are accused of attacking the tone and ignoring the substance of the arguments. Glim and antiGlim leadership proceed into protracted and nasty arguments, until both are highly marginalized, and ignored by the general public. Belief in Glim continues, but when the leaders of antiGlim and Glim finally arrive on a bitterly agreed upon conclusion - the arguments having centered on an actual error in the original formulations of Glim philosophy, they're unable to either get their remaining supports to cooperate, or to get any of the public to listen. Truth, happiness, and all things good never arise, and things get slightly worse, as a result of the error.
Tone arguments are not necessarily logical errors; they may be invoked by those who agree with the substance of an argument who nevertheless may feel that the argument, as posed, is counterproductive to its intended purpose.
I have stopped recommending Dawkin's work to people who are on the fence about religion. The God Delusion utterly destroyed his effectiveness at convincing people against religion. (In a world in which they couldn't do an internet search on his name, it might not matter; we don't live in that world, and I assume other people are as likely to investigate somebody as I am.) It doesn't even matter whether his facts are right or not, the way he presents them will put most people on the intellectual defensive.
If your purpose is to convince people, it's not enough to have good arguments, or good facts; these things can only work if people are receptive to those arguments and those facts. Your first move is your most important - you must try to make that person receptive. And if somebody levels a tone argument at you, your first consideration should not be "Oh! That's DH2, it's a fallacy, I can disregard what this person has to say!" It should be - why are they leveling a tone argument at you to begin with? Are they disagreeing with you on the basis of your tone, or disagreeing with the tone itself?
Or, in short, the categorical assessment of "Responding to Tone" as either a logical fallacy or a poor argument is incorrect, as it starts from an unfounded assumption that the purpose of a tone response is, in fact, to refute the argument. In the few cases I have seen responses to tone which were utilized against an argument, they were in fact ad-hominems, of the formulation "This person clearly hates [x], and thus can't be expected to have an unbiased perspective." Note that this is a particularly persuasive ad-hominem, particularly for somebody who is looking to rationalize their beliefs against an argument - and that this inoculation against argument is precisely the reason you should, in fact, moderate your tone.
This has come up before in other discussions, but Richard Dawkins has converted a not insiginificant number of people. I'm sure that there are people who're put on the intellectual defensive by reading The God Delusion, but I also personally know people who were converted by it, and have heard testimony by people who had been exposed to atheist arguments on many prior occasions who found that The God Delusion effectively addressed their own positions and converted them where other arguments had not.
It's a simple fact that most arguments intended to divest people of their religious beliefs do not work on most believers. Some arguments, and I'm counting presentation as part of an argument, work on some believers, while different ones work on others, but all arguments do not work on most. If anyone had found a reliably effective way of arguing most believers out of their religion, it would almost certainly have been implemented on a mass scale already.
Richard Dawkins' attempts at arguing people out of their religions are mostly unsucessful, but so are everyone else's. I suspect you'd be hard pressed to name an individual who's personally responsible for a greater number of deconversions from religion. Different people respond to different approaches, but if you believe that he's chosen an approach to arguing people out of their religions that ranks low on the effectiveness scale, when compared to other approaches to arguing people out of religion, I think you're mistaken.
I believe his original approach of not trying to argue them out of it at all was a more effective one.
Partly because his argument was so wildly misaligned. His disproof of God is laughably bad from a religious perspective - although it makes perfect sense from an atheistic one. (It makes a number of assumptions about God that few, if any, deists actually agree with.) Partly because of the tone, which sets any reader who has an emotional buy-in looking for flaws which are readily found.
There is a hint there about when a negative tone might be more effective, though - when there aren't flaws to be found. When your opponent is so angry he looks for any possible argument, and finds none.