What you mentioned are by products of the West. Even in the depths of despotism the countries of Europe were the West and countries not populated by westerners were not and now only bear a superficial resemblance to the West. Ask them yourself and see if these countries and their people think of themselves as "Western" beyond a few exportable consumer fads or political fads. Hell we probably are not the West anymore as well since we know spend are time spouting about multi-culturalism and all its hokum. As far as Mexico for the most part it helps refute your first part of your argument, and as for the second part they for the most part are superstitious primitives perhaps better suited to life centuries ago when monsters ruled the land.
Oh, my mistake, I thought we were talking about the unique facets of Western culture that are worth saving. If the free market, individual freedoms, the scientific method, and democratic rule are excluded, I see no way in which Western culture is superior to any other. The Greek traditions and Christianity are superior as a social context exactly because they allowed such progress.
Mexico, and the rest of Latin America, is overwhlemingly Catholic, not animist.