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It meshed very well with the political and social Progressivism of the era, which centered around the believe that history is "progress" and both man and society can be perfected, and that we should strive to do so. Quite a number of Progressives (e.g. President Wilson) were virulent racists, and others (e.g. Margaret Sanger, found of Planned Parenthood and early contraception advocate and suffragist) endorsed eugenics.
Opposition to racism and eugenics, and Social Darwinism generally, was rooted in "classical liberalism," which is what we generally call conservatism now, ironically enough. After the appalling results of the applications of "scientific" theories of the improvement of man in Stalin's USSR and Hitler's Germany, these ideas became anathema, and were more or less quietly dropped from the Progressive's idea box.
Or sort of. They've actually become replaced with sort of a "stealth" version, where the idea is that man is perfectable not by biology -- by appropriate breeding -- but by external means, by education. Nowadays you find the heirs of Progressivism touting education as the universal solvent for human iniquity. Educate a man, they will tell you, and you can turn even the worst character into the best. Conversely, if you fail to educate him, or educate him wrong, you will turn even a saint into a monster.
Conservatives still believe that neither breeding nor education will do that much to alter the character of individual men -- that this is, to a great extent, a mystery thing that we cannot trace 100% to genetics, to parenting, to education, to social mythology, or to experience (although a little bit to all of them). Therefore, while the progressive seeks to perfect man and design a society for this perfect man, the conservative believes man will always be imperfect, and seeks a society that can function well even when its members are flawed.