When I ask this question, I don't mean when book three happens. More so, after the series ends.
Before that, everything she does seems laughable, and everything that does work out for her appears to be pure coincidence.
There are multiple instances where Professor McGonagall expresses her concern for divination itself. For example, after Harry and Ron got up from their seats and Professor Trelawney asks who got up first, Professor McGonagall states:
‘I doubt it will make much difference,’ said Professor McGonagall coldly, ‘unless a mad axe-man is waiting outside the doors to slaughter the first into the entrance hall.'”
Even Dumbledore seems to be slightly irritated at Trelawney during this scene as well.
Obviously, this seems to speak for itself. The book does admit it is a more-or-less imprecise branch of magic.
However, everything Trelawney says (more or less) comes true. Dumbledore does die first of all of the other Professors, Harry does (technically) die in the final book (the Grim), and Umbridge does face something terrible in the near future. My question is, are Trelawney's predictions treated with some sort of respect after the end of the books?
Note: I know she was fired because of Umbridge, but respect is not limited to the school grounds.