Earlier quoted context omitted.
The same negative connotation of "faggot" and "chink" - i.e., that being promiscuous/Chinese/gay/etc is intrinsically bad. I can't speak for the whole world, but in North America at least I've never seen the word "slut" used in everyday speech that wasn't intended to be derogatory. Side note: "purely because it was considered bad 60 years ago for a woman to be promiscuous" I don't think that's 60 years ago, I'm prett…
While I'm pretty sure it was used derogatorily in this case, I've certainly seen it used in a non-derogatory manner. Usually to indicate a sort of unapologetic lover of whatever field. See- http://www.bookslut.com/
However, her mother won't read the blog because of the "slut" part. So I would say that this is derogatory even here.