Perhaps we should dominate, control and punish those evil people who use the available Bayesian evidence when dealing with individuals.

Not nearly all such people are outright sadistic and power-hungry, but those who are can spin complex ideological rationalizations that push the "overton window" and allow the "good" bourgeois to be complicit with a cruel and unjust system.

See e.g. the "Reagan revolution" in America and the myth of the "welfare queen" that's a 3-for-1 package of racism, classism and sexism. I've read a bit about how it has been fuelling a "fuck you, got mine" attitude in poor people one step above the underclass; the system hasn't actually been kind to a white/male/lower-middle-class stratum, but it has given them someone to feel superior to. It's very similar to how the ideologues of the Confederacy explicitly advocated giving poor white men supreme rule over their household as a means of racial solidarity across the class divide.

I also predict that a lot of those evil people will be white, male, and wealthy, so we should focus on members of those groups.

False equivalence. Of course, any movement can degrade into an authoritarian-populist, four-legs-good-two-legs-bad version, given a vicious political atmosphere and polarized underlying worldviews, but... it happens to dominant/conservative ideologies, too! The dominant group just doesn't notice the resulting violence and victimization because from its privileged position it can afford an illusion of social peace.

If we agree that it's a danger of political processes in general rather than of specific movements, could we stop sneaking in implicit arguments that a particular ideology is safe from viciousness and indiscriminatory aggression?

See also: social dominance theory.

Various processes of hierarchical discrimination are driven by legitimizing myths (Sidanius, 1992), which are beliefs justifying social dominance, such as paternalistic myths (hegemony serves society, looks after incapable minorities), reciprocal myths (suggestions that hegemonic groups and outgroups are actually equal), and sacred myths (the divine right of kings, as a religion-approved mandate for hegemony to govern). Pratto et al. (1994) suggest the Western idea of meritocracy and individual achievement as an example of a legitimizing myth, and argues that meritocracy produces only an illusion of fairness. SDT draws on social identity theory, suggesting that social-comparison processes drive individual discrimination (ingroup favouritism). Discriminatory acts (such as insulting remarks about minorities) are performed because they increase the actors' self-esteem.

(More on SDT)

???

Is your assumption that any effort to limit cruelty will necessarily be cruel? Or that SJs in particular are especially untrustworthy? Something else?