"Objectivism" is a narrow philosophy defined by Ayn Rand, a 20th century Russian immigrant to America. Few, even in America, subscribe entirely to that philosophy. However, its influence has permeated a lot of the public discourse, and could be considered an influence on things ranging from the behavior of the Federal Reserve under Greenspan to the direction of the libertarian movement in America. In fact, I'd argue that a primary difference between the modern American "libertarian" brand of classical liberalism and the current classical liberal movements in Europe would be a greater influence of Rand on the American brand. She hasn't been quite as much of an influence on European discourse.
"Social Darwinism" is something that everybody says they're against because it sounds awful and has been misrepresented in exactly the way that OP did. The thing is,
not even Herbert Spencer was a Social Darwinist under that definition. The use of Darwinism by classical liberals to relate to public policy originally said something along the lines of: "Without interference, production will usually tend to improve, because better producers are more fit to survive." Nothing like: "Only fit people should survive, the rest should be in poverty and/or die." So, in America, Spencerian classical liberalism is indeed a common philosophy, and it is in Europe too, wherever you find classical liberals (like the Dutch PM or the Estonian PM for example). But "Social Darwinism," the straw man created by opponents of classical liberalism? Of course it's common nowhere.