Different theorists who divide the world into "Civilizations" categorize Latin America as either a part of Western Civilization are simply as Latin America. The controversial Samuel Huntington explicitly excludes Latin America from the Western World in his divisions of world civilizations. Other theorists like Arnold Toynbee, who did extensive historical analysis on the rise and fall of civilizations, concluded the world was divided into 4 surviving civilizations; Western/Orthodox/Byzantine, Islamic, Hindu, and Eastern, and explicitly included Latin America in the Western World.

Other theorists divide the Western World into 5 components; Europe, Anglo North America, Latin America, the Caribbean, and Oceania.

Then again the terms "western" "western world" and "civilization" are incredibly politicized and these theories are highly controversial, including the theory that the world can be divided into "separate civilizations", which many consider to be bunk and meaningless.

PS: Why is /r/HistoricalWhatIf a private subreddit?

The top mod threw a temper tantrum, kicked out everyone and set it private. The rest of the mod team recreated it as /r/HistoryWhatIf.