Were the Nazis right or wrong to use evolution to justify their philosophy?
I think they bent it until it was unrecognisable from the facts.
They 'used' the science of evolution in the same way a homoepath uses physics to explain their quackery. Not at all, not very well, with a handful of misunderstanding and a sprinkle of bull****.
Science is about facts not values. The Nazis used values to distort facts, for example alturism is just as important as competition in many species. I think applying physiology to the study of social behaviour is not entirely wrong, however when it is done in accordance with science it is usually supportive of a more liberal position.
The Nazi doctrine of genetics and natural/Sexual selection is very skewed. It was an common believe that society could shape specific human traits like intelligence through 'positive' eugenics. This was often the case in the late 1800s after Francis Galton (an brilliant Statistician IMO, invented the regression line and Normal/Binomial Distribution) published an book on Human Inheritance. Some popular statesmen, business and even philanthropists in the Anglo-Germanic world (like in the USA and Germany, not so much in Britain despite being the birth place of Eugenics) believed that mental disabilities and physical handicaps could be breeded out by artificial selections. It never really started of an mainly racial topic. But as new age imperialism (boosted by the Second Industrial revelation in N.America and Germany as well as N. Europe in general) dawned, some believed that the technological distance between the coloured people being colonised and the Europeans of 'Nordic Anglo-Saxon' stock were largely due to genetic reasons and that the coloured man could never be 'civilized' because they are inherently inferior. Nevertheless modern Genetics have proven much of these foolish presumption out of mainstream science. We now know that Mental and Physical disabilities are the results of genetic mutation that is caused by damage by DNA rather than simple inheritance of traits. You cannot stop gambit sex cells from mutating. All modern Homo Sapien population are recent arrivals from E.Africa.
Simply put, Darwinian evolution and modern genetics is very much against the idea of a master race. The idea of a perfect, unchanging master race makes absolutely no sense and is grounded in nothing but superstitious nonsense.
Darwinian evolution would suggest a well adapted genetic group for a particular time and place.
Mother's biology is inherited by the child and in my opinion this impacts upon the child much more than genes do. A person's biology can be changed, mostly through diet, but as most people eat 'stereotypical' food, their biology does not change all that much.
An example is Indians. They incline towards vegetarianism, which has disastrous consequences on health. Not eating meat deprives the body of zinc and leads to a reduction of testosterone and an overabundance off oestrogen. The men are less manly and less capable of defending themselves. India's shameful martial history reflects this.
However, the country continues to incline towards vegetarianism, and so the population that does not eat meat exhibits the symptoms of low testosterone.
Humans are biological machines that need a specific set of inputs to really prosper. I suspect that genes are much less relevant to a race's superiority or inferiority than diet.