All three ideologies have certain key elements in common.
Their entire worldview is based on an in-group/out-group concept: the Chosen Race/the Goyim, the believers/the kuffar, the workers/the exploiters.
The in-group/out-group polarisation is portrayed in terms of purity. In some cases this is quite literal: the out-group is seen as a physically contaminating influence. In other cases, the impurity of the out-group is less tangible. They are pathologised and dehumanised, depicted, often using disease metaphors, as pervasively immoral, bestial, even demonic: the Islamophobes, the antisemites, the capitalist exploiters.
A lachrymose victimhood narrative is constructed in which almost all events, either historically or in the present day, show the in-group being oppressed by the out-group. It is a permanent, dynamically-adapting conspiracy theory, almost infinitely resistant to countervailing factual evidence. This narcissistic sense of past victimisation provides the emotional warrant for ruthless action against the supposed victimisers.
Members of the in-group have a duty to strive against the out-group, overcome them and establish supremacy over them.
The eventual triumph of the in-group over the out-group is seen as inevitable. History ineluctably moves towards that conclusion. The out-group may seem strong now, may win successes here or there, but their defeat is assured. The in-group just needs to bide its time.
The "laws" or teachings that describe or regulate the differences between the in-group and the out-group are seen as somehow arcane, a "secret science" beyond the understanding of the ordinary person. Thus "guru" figures are required to interpret them and explain them to the "masses". This encourages an authoritarian mindset, an anti-democratic "submission" mentality, in which leaders consider their flocks unfit to make important decisions and the followers accept their own unfitness. This stands in contrast to post-Reformation Christianity in which every individual is expected to question and to seek understanding.
There is a strong sense that where the in-group has already triumphed, the out-group must not be allowed to recover, or "regain territory" so to speak. There is no need to "play fair" in these areas. Harsh, persecutory measures are justified to prevent the out-group rebuilding its strength, since this would be an anomaly running against the "inevitable" flow of history. Thus we see Muslim irredentism in formerly Islamic territory, such as Spain, the ruthless persecutions of the Communist regimes against "class enemies", the endless warnings from Jews of a "resurgent" antisemitism in need of repression that should somehow be exempt from the normal rules of free and open discourse.