In the real world, the culture of white supremacy was deeply damaging to impoverished white people after the Civil War. The hostility that American apartheid created between poor whites and blacks, meant that these two oppressed groups were unable and unwilling to join together to consolidate their power and demand major concessions from the ruling class. This is why to this day, the United States has never developed a labor party, and why the U.S. has never developed the kind of comprehensive welfare state enjoyed by European nations that embraced social-democracy. To this day, levels of economic inequality are much higher and more oppressive for whites in America than for whites in European social democracies. Bigotry can be deeply self-destructive for the bigot.
So, no, I have no problem with the idea that the Zhat Vash's bigotries might lead them to some truly self-destructive behavior. Especially since "Broken Pieces" and "Et in Arcadia Ego, Part I" made it very clear that the Admonition causes brain damage and severe cognitive distortions in humanoids -- we literally saw Romulans commit suicide and self-mutilation after being exposed to it.