What do we call a person who cannot read people?

That kind of person is "socially inept."

http://www.urbandictionary.com/define.php?term=Socially+Inept

socially clumsy where clumsy, in particular:

awkward in movement or in handling things.

Perhaps you are looking for insensitive (or unsensitive), or not sensitive, as in the sense of "not being responsive to or aware of feelings, moods, reactions". Also, perhaps you can use unempathetic.

A "poor personality decoder", not exactly an idiom but conveys the idea.

You might also say "ingenuous" or "naïve".

• ingenuous (adj) - (said of a person or action) innocent and unsuspecting. Google

• naive (adj) - deficient in worldly wisdom or informed judgment; especially : credulous MW