This actually seems confused to me. It may well be that contempt is an inappropriate response to someone who suffers an actual mental illness. Some kind of compassion seems more appropriate, and of course we would know better than to get into an argument with such a person. We might humour her, but we would not try to argue with her. Fine so far.
The view has it that those who are contemptible are not worthy of respect. This seems true as far as it goes. But notice that to hold a person in contempt is to ascribe to him a capacity for responsibility. Accordingly, we do not hold the mentally deranged in contempt for their delusional beliefs; rather, we see their beliefs as symptoms of their illness. To see religious believers as proper objects of contempt, then, is to see them as people who should know better than to believe as they do. It is hence to see them as wrong but, importantly, not stupid. Thus it is a confusion to regard religious believers as both contemptible and cognitively beyond-the-pale.
But you can be cognitively beyond-the-pale for all sorts of reasons that fall short of an actual mental illness. Generally speaking we express admiration (or esteem) for people who have qualities that are admirable (and note that judgments about what is "admirable" don't have to be objectively binding on all rational creatures, they are made relative to shared values, purposes, etc.). They are people who have certain excellences, which might, in context, include intelligence, intellectual honesty, courage, openness to new ideas, and so on. We feel contempt for people who lack such excellences or who actually have the opposite qualities. If we find ourselves arguing with someone who is stupid, intellectually dishonest, fearful, and close-minded, it is perfectly appropriate to feel the opposite of admiration - i.e. contempt or disdain - for her.
Someone with those qualities may well be cognitively beyond-the-pale in the sense of being impossible, for all practical purposes, to persuade by rational argument. She may be beyond the reach of reason. We would do well not to waste time arguing with someone who possesses that particular combination of qualities. But that does not entail that we are wrong to regard her with the opposite of admiration. She clearly has qualities that are the opposite of the relevant admirable ones, i.e. she has qualities that merit our contempt.
I conclude that there is nothing at all confused about regarding some people as both cognitively beyond-the-pale and contemptible. Indeed, the very same qualities may make somebody both of these things.
This is kind of tangential, but the Aikin/Talisse passage puzzled me the first time I read it ... and it still puzzles me. I'm not actually arguing that we should feel contempt for anyone in particular. I certainly don't think that we should feel contempt for all religious believers. But I don't accept the claim that "contemptible" and "cognitively beyond-the-pale" are mutually exclusive categories.
It's also possible that someone who merits our contempt - the opposite of our admiration - nonetheless also merits some minimal or residual kind of respect as a fellow human being or a person (in the Lockean sense) or a sentient creature, or some such thing. I.e., the person is due some kind of residual regard for her interests. That opens up a large set of issues about what it is to respect somebody. But this sort of minimal/residual respect can co-exist with the idea that, at least for current purposes, the person is the opposite of admirable and that it's worth expressing that evaluation.
Again, I conclude that someone can both (1) be cognitively beyond-the-pale and (2) have qualities that are the opposite of admirable - and merit expressions of contempt. Even though this person is still owed some residual regard for her interests, that is a separate issue.