The NAZIs did believe in social darwinism and eugenics
The right wing of the republican party belives in social darwinism also.
Not sure what your point is?
Keep in mind that there is no contradiction as you surmise because along with the idea of creationism and Intelligent Design is the concept of a Designer or God, and so with a higher power to answer to, values are not shaped by purely methodological naturalism, which the NAZIs felt led to their values, and that their values were scientific whereas believing all men are equal in terms of having the same rights, they would argue is not scientific, and is a perversion of truth.
This has nothing to do with god or religion. It's just another example of group elitism.... "my group is better than yours". Some people use things like "The bell curve" to say whites are smarter than blacks. Some people use the "bible" to say christians are better/more moral than non-believers. People have always used various reasons including science and religion to prove their group is better than others throughout history.
Crusades
Manifest Destiny
Inquisitions
Holocaust
Ethnic Cleansing
etc, etc, etc
I personally think the Nazi's get a bad rap for someone being the worst thing that ever existed. Don't get me wrong; the Nazi's did a lot of bad things (I'm certainly no holocaust denier)...... but there are a lot of other groups that also did a lot of bad things. Stalin and the soviets, Genghis Khan, the persian empire, Americans (eradicating virtually all indigenous people), spanish conquistadors, etc. etc. etc. The Nazis are just another example of a group that did bad things to other people