Dennis Prager points out that all punishment contains revenge.
People on the right are not as horrified by revenge as people on the left because the right wants to strongly punish norm violators.
Other distinguishing features of the right include a reflex that traditional ways of people (such as the nuclear family) are better than untested ways, and more comfort with hierarchy and inequality.
David Remnick writes in The New Yorker:
Amos Harel, a military and political analyst for Haaretz, said that one of the most dispiriting aspects of the current nightmare is the way Sinwar was able to provoke the Netanyahu government into a state of horrific and ruinous fury. “The sense in Israeli society is that we are going down the drain, and Sinwar has helped drag us there,” Harel told me. “When we justify things we never would have justified before, we are in the moral gutter. Words like ‘revenge’ used to be heard only among the Bezalel Smotrichs and the Itamar Ben-Gvirs of the world”—two particularly reactionary ministers in Netanyahu’s cabinet. “Now military units and mainstream colonels are using terms like nekama, revenge. It’s almost part of the norm now. I am not sure it was part of Sinwar’s great plan, but that is where we are.”