One 2017 paper does try to correlate the dark tetrad (narcissism, Machiavellianism, psychopathy, and everyday sadism) to extremist political views:
Previous research on personality and political attitudes has been conducted in countries where political parties from the center dominate the political system. In the present research (N = 675), we focus on the relationship between the dark side of human personality and political orientation and extremism, respectively, in the course of a presidential election where the two candidates represent either left-wing or right-wing political policies [Austrian presidential election of 2016]. Narcissism, Machiavellianism, psychopathy, and everyday sadism were associated with right-wing political orientation, whereas narcissism and psychopathy were associated with political extremism. Moreover, the relationships between personality and right-wing political orientation and extremism, respectively, were relatively independent from each other.
Going the other way around, a 2019 review of research on the psychological profiling of extremists doesn't quite tie them with any particular personality (disorder) but it does generally correlate them with psychological distress:
Empirical findings support a relationship between psychological distress and extreme political ideologies. Compared with moderates, political extremists—on both the left and right of the spectrum—report stronger anxiety about their economic future (van Prooijen, Krouwel, Boiten, & Eendebak, 2015). Furthermore, extremists are more suspicious than moderates about governmental institutions, suggesting distressed expectations of these institutions (Inglehart, 1987). Experimental findings are consistent with these insights. For instance, people psychologically compensate for feelings of uncertainty and fear through strong ideological convictions (McGregor, Prentice, & Nash, 2013), and inducing a loss of significance increases extreme beliefs on both the left and right (Webber et al., 2018).
The link between psychological distress and political extremism is inconsistent with the assumption of the rigidity-of-the-right model that psychological distress stimulates conservative ideologies only. We note, however, that psychological distress stimulates a preference for leaders who, in addition to being radical, are also group-oriented (Hogg, Meehan, & Farquharson, 2010). Feelings of distress therefore make political currents that are not only extreme but also nationalistic particularly appealing. Indeed, the majority of studies indicating a right-wing shift under conditions of uncertainty were conducted in Western countries where the political currents that combine radicalism with nationalism happen to be right wing (e.g., the United States, several European Union, or EU, member states; Jost, 2017). Would distress exert similar effects in countries where the political currents that combine radicalism with nationalism are mostly located on the left, such as Venezuela (i.e., Hugo Chavez and Nicolás Maduro), Ecuador (i.e., Evo Morales), or Nicaragua (i.e., Daniel Ortega; e.g., Müller, 2016)?
The review paper goes to discuss "cognitive simplicity" (by this they mean a black-and-white perception of the social world), overconfidence, and intolerance as other established (if somewhat obvious) psychological traits of extremists.
I guess a tentative conclusion from this might be that personality abnormalities (beyond those discrete traits) don't feature high on the psychological profile of extremists (i.e. there might a few psychopaths among the extremists, but most extremists might be just "suffering" from those four discrete traits). Or perhaps more research is needed.
