The easiest way to see this, if you grew up in the U.S. and have not traveled much, is to read tourist guides for your own country.
Generally, people overestimate the variation in their own compatriots and underestimate that in foreigners.
I'm having a hard time matching your generalization with my experience. When I started travelling I was surprised how similar people were regardless of where they were from.
Sure you can dig into political views and find themes but those aren't consistent or pervasive enough to make predictions on an individual basis.
You might as well say "can you identify someone's cultural heritage without discussing anything that would allow you to identify their cultural heritage?". This stipulation makes the task definitionally a matter of chance.