I'd like to see what they say about me. I bash both parties all the time. My comments on every subject are usually sarcastic. Do they have a working sarcasm detector? Or is it all about the things you follow? George Takei is a gay rights activist. So would a conservative who likes ice cream (ben and jerrys) and George Takei be labeled liberal?
Or is someone who is far-left who attacks Hillary going to be labeled conservative for being anti-Democrat?
They could also look at your friends and their affiliations, your likes, the articles you read, how other people respond to the things you post, etc, etc.
They might have you completely wrong, but without knowing their specific approach or how much data they're using it's hard to say which people they will get wrong (or right).
I've seen those types of labels applied. They never work. I got rejected from a minimum wage job in college because the chain store had a standard questionaire. If you answered that you don't use drugs, but think they should be legal, you were considered a lying drug user. The makers of the test couldn't conceive of someone who thinks drugs should be legal and regulated, and wouldn't use them if they were. Though, this was 20+ years ago, so the modern legalization swing wasn't popular yet.
I'm not sure proof by incompetently written questionnaire holds.
I can only think that the labels are wrong much of the time, and the effectiveness of them is over-stated to increase Facebook's ad income.
The labels don't have to be perfect to help FB. Even if you've correctly categorized only 50% of people into one of three broad categories that's still very valuable information for advertisers.