What Suber calls logical rudeness is a response to criticism which insulates the responder from having to address the criticism. Suber comes up with a taxonomy of logical rudeness:
The primary type is probably the application of a theory of justified dismissal, such as a theory of error or insanity, to critics and dissenters. Another major type is the interpretation of criticism as behavior to be explained rather than answered. This is closely connected to the type that refuses to see a meta-level in the critic's criticism, and will not allow critics to escape the object-language of the theory. A rude theory may reinterpret criticism as a special kind of noise, or as unwitting corroboration. A theory may evade criticism without rudeness by postponing as answer or referring the critic to the answer of another. The abuse of postponement may be rude, however, as when the motions of postponement are made shorthand for dismissal, or when the subsumption of an objection under a larger system of belief is made shorthand for refutation. A rude theory may be held for reasons other than its correctness, such as the support for the believer shown by voters or grant-giving agencies. A weak sort of rudeness lies in any unfalsifiable theory, and a strong sort lies in boon theories which identify critics as nonpossessors of a special boon. The theories of justified dismissal and the boon theories tell critics that they are disqualified from knowing truth or even deserving answers because of some well-explained foible or fault in themselves. All the types have in common an evasion of a responsibility to answer criticism on the merits, when that evasion is authorized by the theory criticized. All types are triggered only by expounded criticism, and only insulate the proponent from conversion or capitulation, not the theory from refutation.
There's the potential for this sort of thing in anyone with a belief whose scope is broad enough to explain why some other people don't believe it. As mentioned previously, some Christians tell atheists that atheists know there's a God really and are just being atheists to annoy, because they know it teases. Some atheists tell religious people that theists won't accept atheistic arguments because they're afraid of death, or too immersed in the church community to bear the social cost of leaving. In a conversation about race or gender, it won't be long before someone claims another person's view is held because of their privilege. And so on.
Suber calls this rude rather than fallacious because it is possible for people who hold true beliefs to be "rude" in this way (and in fact, rejecting arguments because they come from rude people is itself rude). Rather, rudeness violates the norms for debate, but by those same norms, we'd like even people who hold beliefs which lead them to be rude to be able to join in.
In Suber's taxonomy, some sorts of rudeness seem worse for debate than others. Towards the end of the essay, Suber distinguishes "fixed belief" from "critical belief", the difference being whether the believer is prepared to concede that they might be wrong. Suber says it's not clear that critical belief is possible or desirable in all cases. In particular, it seems to me that people who regard disagreement as a moral defect will find it hard to be critical believers.
Suber wonders about the value of debate (by which I assume he means the general to-ing and fro-ing of philosophical conversation, not merely formal public debates). It seems to me that this value partly lies in reducing the problems of filtered evidence. We ourselves filter the evidence we search for, but a multi-sided debate might serve to correct this. One way of squaring a desire for debate with beliefs which justify rudeness might be to admit that we hold such beliefs, but to avoid rudeness itself as a tactic. Beliefs which justify rudeness might legitimately influence whether we want to have the debate at all, but once committed, it seems worth holding our own beliefs critically.