Paul Katsafanas has an interesting paper on fanaticism at Philosophers' Imprint. In it he argues against what he calls in the Enlightenment account of fanaticism (which in the Enlightenment would have often been called 'enthusiasm'), which he characterizes as involving the following three elements:
(1) unwavering commitment to an ideal
(2) unwillingness to subject this ideal to rational criticism
(3) presumption of non-rational sanction for the ideal
I think you could criticize this as an account of actual Enlightenment views of the matter in a number of ways -- 'non-rational' is too vague, and while there is no single account of enthusiasm in the early modern period (and I am not as inclined as Katsafanas to think that Locke, Hume, Shaftesbury, and Kant are as much in agreement as he suggests), people discussing the matter tended to think of it in terms of principles, not ideals, and it tends to be important for how the word 'enthusiasm' functions in discourse that it is not merely a rejection of rational criticism but also a rejection of authority. Enthusiasts got the bad name they did because they were seen to subvert the structures of authority maintaining society. Hume, for instance, often uses this aspect of the idea in his historical explanations in the History; it's also why people were often nasty to Quakers and Methodist revivalists. They were seen as disrupting the order of society, and it's not merely that their grounds were seen as non-rational but (which is a different thing) that they could not be reasoned with. To be sure, there was a common notion of a 'harmless enthusiast'; but not everyone would have accepted such a view, and the harmlessness would be because they were, as we would say, a bit crazy -- authority and reason don't work on them but not because they are deliberately trying to overturn them.
This is not a purely historical issue, not that there are ever any such in matters of philosophical analysis; Katsafanas's immediate criticism of the 'Enlightenment account' is that it does not capture the intolerance and dangerousness that these very thinkers thought was attributable to enthusiasts. But the obvious reason for that is that the 'Enlightenment account' he gives is incomplete. But one can imagine someone trying to generalize an account of enthusiasm/fanaticism based on various early modern comments and coming up with something like this as a first approximation, so it's not an immediate issue for analysis.
As Katsafanas notes, however, 'the Enlightenment account' will not work as an account of fanaticism itself, because it includes too much. It covers anyone who is a 'true believer', in the colloquial sense. Katsafanas still regards 'being a true believer' as a rational defect, but it's so common that I'm not sure you can even go this far. We usually think of sports fans and music fans as 'fans', i.e., fanatics, by a figurative and hyperbolic extension of the term, but most fans of anything would count arguably count as 'true believers' in this sense. People are just resistant to criticism of their likes and dislikes in matters they regard as closely intertwined with who they are, even if reason didn't itself have much to do with their liking/disliking it or regarding it as a part of who they are. And while this can no doubt lead in bad directions, in itself this nonreasoning resistance seems to have nothing unreasonable about it. It's not a rational defect merely to have strongly decided tastes.
In any case, Katsafanas goes on to argue that we need to add several additional elements to get an adequate account:
(4) adoption of one or more sacred values,
where 'sacred values' means 'values that are associated with characteristic emotions like love or dread and are regarded as uncompromisable and indubitable',
(5) treating these sacred values as necessary for preservation of self-unity,
where this is his somewhat odd and controvertible way of saying what would perhaps more colloquially say as conveying that these sacred values are 'essential to your identity'.
I take it that Katsafanas is using these as steppingstones to try to build up an account where one can see how the elements would combine to make fanaticism dangerous; it's certainly not the case that these on their own add much. I take it that most people would have already assumed that element (1) implied something more or less like these, with these at most clarifying it so that we can cut out some marginal cases. So far we still don't have anything to distinguish fanaticism from many cases of (say) wholehearted love of one person for another. Katsafanas continues, however:
(6) taking these sacred values to be threatened if not widely accepted
(7) identification with a group that has these sacred values as shared values.
These both are definite advances; they give us an account of fanaticism that is social in character.
Katsafanas often talks about his account as taking fanaticism to be characterized by (1)-(7), but I'm honestly not sure why he doesn't take (4)-(7) to replace rather than add to (1)-(3); that is, given his arguments for them, I don't see what is missing in (4)-(7) that would require (1)-(3) specifically. At the end he seems to suggest that (4)-(7) introduce something like a disposition to violence, but, as I will go on to say, I don't see how that is supposed to work. This should be kept in mind as a qualification for the rest of my criticism of his account -- it's conceivable I'm not grasping something about how this account is supposed to fit together.
It seems to me that all Katsafanas has done is taken the 'true believer' of the original and made him or her a 'socially participant true believer'. What he has not given is what he promised to give, an account in which it would be clear why intolerance and dangerousness tend to be associated with fanatics. Consider a person who is not a fanatic but a fatalist. They have some sacred value -- say, liberty under a certain conception -- and they see the upholding of this value as essential for making sense of who they are as a person, and they recognize (as you usually have to with conceptions of liberty) that this liberty is threatened and not widely accepted, and they participate with groups that take this liberty as a shared value, but they honestly don't think they or the group have any ability to change things. Perhaps they are a dwindling minority and the fatalist just thinks that, alas, society is by this point doomed and there is nothing that can be done about it -- they will certainly lose, and no action they can take will change that, but because the value is uncompromisable and true, they will stay the course to the end. Now, this person by Katsafanas's definition is a fanatic, but it's really odd to classify them as such, because we don't think of merely being resigned to failure as a fanatical attitude, and obviously we don't because it isn't. As we might put the point, intolerance and dangerousness are associated with fanaticism because fanatics do things, but the resigned fatalist isn't doing anything. Being resigned in the face of (as you see it) the whole of society going mad isn't fanaticism. That is, the only component of Katsafanas's account that is not purely a matter of mental belief and attitude is identification with a group, but mere self-identification, even combined with the mental components, doesn't give you any fanatical acts. It's compatible with almost anyone you know being a fanatic, which they express entirely by having a poker night with other fanatics. I mean, there are groups with a history of breeding fanatics that often do a lot of social events together, like the KKK or Antifa, but it's not having brunch at the local eatery together that makes them identifiable as fanatics, but rather the willingness to engage in terroristic acts and assaults.
Perhaps Katsafanas assumes that adoption of sacred values combined with a sense of their being threatened always issues in definite outward actions, but this I think is just false, psychologically; at the very least, it would depend on the "characteristic emotions" involved and the opportunities for expressing them. Given his emphasis that fanaticism is a propensity to violence, not necessarily actual violence, I suspect that Katsafanas thinks more specifically that (1)-(7) tend to issue in violence, but this is a fortiori not true, as we see in the case of the resigned fatalist. You don't even have to go so far as resignation; sometimes people are still just trying to sort out what, if anything, they should do; sometimes people respond by not interfering with others but trying to move away from them and start over; and so forth.
I should say that, although Katsafanas doesn't consider these cases in particular, he ends the paper by considering the possibility that the content of the value might interfere, for instance if someone's sacred value were freedom from coercion, in which case you would have reason from the sacred value itself not to act violently toward other people over it. But since such people could meet (1)-(7), and he says that such people would not be fanatics "or at least not wholeheartedly", this seems to make his account defeasible, so that you could fit all of the criteria and yet not be a fanatic. And at least one argument he used to reject the 'Enlightenment account' -- that it would make peaceful Buddhists and tolerant Christians fanatics -- would seem to apply to his own account. It's not as if the difference between nonfanatical Buddhists and Christians and fanatics is that the former don't have deeply held sacred values, or that they don't join groups that share those values, and nothing seems to prevent them from thinking those values under threat, so we seem to be stuck in the same place we were, except with a social component that doesn't affect the original problem.