Argentina and Uruguay are white settler societies. If they aren't western, then neither are the United States and Australia. The former at least is far less white, and in all the aforementioned countries, the indigenous are a powerless, marginalized, tiny minority. That's much less the case in most of Latin America. Most of Latin America outside of the Southern Cone has Hispanic Cities and a largely indigenous countryside. To return to the Mexico example some have brought up, Mexico City and the resort cities on the coast are clearly culturally Western, but the rest of the country, not so much.
The fundamental lack of liberalism in Argentinian polity is, indeed, making Russia the closest comparison.
Spain and Portugal were at least as lacking in liberalism until the 1970s, and almost everyone agrees that they are part of the West.