Coming back to this topic to note a bit of new information. Now we know that Poppy Pomfrey is not only an ally and a benevolent figure within the school, she is an Order member as well. () That's very encouraging.

Given this, I wonder if Madam Pince is also an Order member or merely a benign figure. I'm considering that she was the first to be assigned Hermione's service and that she seemed so open to give Hermione tasks that would allow her to self-tutor and that put sensitive materials in her hands. (The counter example, of course, is boot's placement with Carrow, so perhaps these assignments are no good indicator of allegiance.)