Cherry-picking Nazi ideology for political reasons

There are a number of problems with the argument that we shouldn't study the biological sources of behavior because such an approach led to Nazi atrocities against other races, but one criticism I haven't seen is that people arguing such a position are cherry-picking convenient Nazi beliefs. 

The core Nazi belief was public health--a healthy social organism in its proper relationship with nature. The social body will be healthier if people live healthier lifestyles; if they keep their bodies in shape through exercise and getting fresh air; if they eat wholesome, natural foods that are free of additives, preservatives, and other man-made toxins; if they avoid tobacco, alcohol, and meat; if air and water pollution are eliminated; if there are advances in private and public hygiene, advances in medical science, and access to current treatments. 

Concern for collective health was absolutely at the center. As one specific part of that, Nazis believed that the social body had to be treated for some illnesses by the elimination of diseased elements. They viewed the mentally handicapped, the mentally ill, and the terminally infirmed like cancerous cells. Likewise, Jews, Gypsies, homosexuals, Communists, and Slavs were seen as pathogens attacking the German body. The social organism is made healthy by killing off the germs. 

As people who were focused intensely on nature, Nazis believed in respecting the ecologies they lived in. (Ernst Haeckel, a scientist whose ideas inspired Nazism, coined the term ecology). Nazis were conservationists. They advocated the preservation of fauna and flora. They fostered a love of nature. They passed laws against cruelty toward animals. Vegetarianism was encouraged. Researchers were forbidden from doing certain kinds of animal testing. The penality for killing an eagle was death. The social body could not be healthy in a sick environment. The overall theme was health through harmony with nature.

If Nazi ideology led inexorably to the gas chambers, the belief in goverment advancement of public health is much closer to the center of that ideology than is the belief that biology influences human behavior. The truth is that Lefties link human biological research to Nazism because such research works against their claim that society can be fixed by social and economic reforms. They cherry-pick the Nazi beliefs that advance their politics. An honest Lefty like Jonathan Spiro (from whose book Defender of the Master Race much of the above facts are taken) admits that collective health and harmony with nature was their obsession. I wouldn't claim that prioritizing public health logically leads to mass executions, but arguing like liberals do--that Nazi-like thinking leads to Nazi-like behavior--leads to that conclusion. (I will concede that some conservatives make these kinds of arguments too. Their reasoning stinks just as much).