The pronoun that may have a long history of referring to people as well as things, but using it can sound illiterate in some contexts where you’re obviously referring to humans—a habit that writers have picked up from spoken American English. Further, despite the long use (or misuse) of that in connection with people, current English textbooks maintain that who should be used to refer to people or to animals with names or special talents. That and which, they say, should be used to refer to animals, things, and sometimes to anonymous or collective groups of people.
A few exceptions exist, as usual. Using that instead of who can sometimes get you out of a tough situation, like this one:
“Did she say it was a man or a book that she curled up with last night?”
I could make an inappropriate comment about this sentence, but this time I’m gonna restrain myself.