Up two the last sentence you seem to be in perfect agreement. The last sentence merely adds that the actors in science may color their studies, results, interpretations, to make unscientific points. Many a scientist thought they were proving differences in e.g. intelligence between the races, up to and including some of the Nazi's horrors. Doing in vivo lobotomies to show Jews are inferior may be scientific, but that is very far besides the point.
The "natural social order" for humans isn't scientific because there is none that we can identify, unlike in animals with much simpler social structures. Social Darwinism isn't based on evidence, being promoted by quacks that are anti-science.
You're trying to draw a distinction where there is none.
Science is the way to seek truth. And yes, we should use scientific evidence to reject anecdotes, if that evidence is strong enough. Not sure what you mean in your last sentence but it sounds wrong to me.