Is "Latin America" part of the "west"?

[Verily]

Yes.

I consider "The West" to a be a socio-cultural institution, bound up in European history, Catholic and Protestant Christianity, etc. It includes Western and Central Europe and all of the Americas, as well as Australia and New Zealand. It does not include, however, other wealthy and powerful countries unconnected to that history, such as Japan and Korea.

This is in contrast to "The First World" or similar terms based more on economics and politics, which would include places like Japan and Korea (and Taiwan, Singapore, etc.) but exclude, say, Bolivia or Guyana or Nicaragua (although Chile, Argentina, Uruguay and Brazil have at least an argument to be included these days).