Do you think that the majority of liberals are atheistic and that most Christians are politically conservative? No doubt, many liberals are atheists and some Christians do lean towards the right. However,
this table seems to suggest a more complex picture in which the political leanings of faith groups in the United States vary enormously, from Mormons (70% preferring the GOP) to the African Methodist Episcopal Church (92% leaning Democratic, a higher proportion than the 69% of atheists who lean in the same direction).
Yes, moral relativists tend to reject the idea of moral absolutes - which is not the same thing as "having no right or wrong". Whether you are a religious believer or an atheist, you can believe that killing is generally wrong without believing that it is always wrong (such as a killing in self-defence.)
How can the left say that white supremacy is evil? For the same reasons that many conservatives would say that white supremacy is evil. Because it is based on a false claim - disproved by scientists long before you or I were born - that there is such a thing as a white race. Because it violates the moral principle that discrimination is wrong. Because, for many Christians, Christian teaching supports a belief in the equality of humans, not in the supremacy of a group identified by the colour of their skin.
You have linked Nazism to big government socialism. Yes, the Nazis used socialist ideas. However, their programme of big-government spending on public developmens such as roads was not the reason why people reacted in horror to their conduct and said "Never again". Holocaust memorial museums tend to say that the way that Nazis convinced their supporters to attack Jewish people and to participate in industrialised mass murder has a lot more to do with their white supremacist and fascist thinking than their ambitious plans for new roads and other infrastructure.
You suggest that the left is obsessed with race. Many people on the left are certainly concerned about racism. When extremists chant "Jews will not replace us" and the slogan "Blood and Soil" as they march, identifying themselves with anti-Semitism and a political movement which murdered millions, is it surprising that some people on the left would want to protest against that?