Left and right being global descriptors in politics is especially complicated when trying to explain Latin American politics to my fellow Europeans and North Americans. The term really only applies to certain societies and doesn't explain the populist movements that have traditionally represented the working classes in these countries. But those movements, as well, are losing popularity thanks to the rise of the far-right that has managed to portray itself as a revolutionary force, much like socialism in the 20th century.
Your point about a local focus is interesting! I do think the far-right also has a globalist message, in its own way, even in all its nationalism. The same talking points, from anti-vaxx to climate change and immigration, repeat themselves around the world. But to beat them, you need to reach people on a personal and local level.