But any readily observable characteristic would either manifest as something illegal to discriminate on (sexual orientation, weight, sex, appearance, etc.) or as something not illegal to discriminate on in the first place.
Illegal discriminatory hiring practices are very specific, so suspicious or not, it doesn't matter. There's no legal grounds for someone to sue a company because they used Facebook to determine that they don't like "Fight Club" or that they eat a lot of Burger King and were thusly not hired.
On FB you could easily see someone's sexual orientation, for example, or the year they graduated. It's better not to look. If you hire them and you get on outside work, then by all means add them as friends and you can see all you want.
Illegal discriminatory hiring practices are very specific, so suspicious or not, it doesn't matter. There's no legal grounds for someone to sue a company because they used Facebook to determine that they don't like "Fight Club" or that they eat a lot of Burger King and were thusly not hired.