If the KKK has nothing to do with Christianity, could you also say that ISIS has nothing to do with Islam? Could you say that NK has nothing to do with atheism? I think that you get my point.
The KKK are Christian terrorists, but Neo-Nazis generally aren't Christians and misc. alt righters religious views are varied.
Trying to create an equivalency between violence perpetrated by Muslims and violence perpetrated by Christians is dicey because, for reasons not necessarily related to the religions themselves, weaponized Christianity has generally been used as a means to other ends, whereas weaponized Islam has almost always been carried out for Islam's sake.
Maybe if Jesus - like Mohammed - had been a military leader who created an empire and forcibly converted all in his path, that would have been different. But he wasn't. There was never a "Christian empire." Even things like the Inquisition were more about earthly monarchs wanting to consolidate power. When Europeans engaged in imperial conquest, they sometimes said they were doing so "for God" but in practice, they were far more interested in getting land, natural resources and forced labor.
When right-wingers use Christianity as a weapon, it's because they view Christianity as just one of many things that make "the Volk" what it is. When Orthodox Serbs slaughtered Muslim Bosniaks, they weren't doing so "in the name of Christ." They were doing so because they were Serbs, and being Christian was merely a part of what made Serbs, Serbs (and being Muslim was merely part of why Bosniaks could never be Serbs and never be permitted to exist in their nation-state).
Christians do not feel any particular "kinship" with Christians as a whole, in the way that Muslims do with the "ummah" - the community of believers. A white Southern Baptist could care less about Christians getting killed or persecuted in Nigeria or Iraq. Those Christians aren't "their people" (Western white people) so it doesn't bother them.