To begin with, Offred does not fit into society because she expects more of herself. She remembers a life when she expected a different future. She is not pleased with her lot, to be a handmaid. However, it seems to be a society where no one would fit in. Offred is just more willing to complain about it, at least to the reader.
For proof you will want quotations. Here is one from chapter 5.
"There is more than one kind of freedom...Freedom to and freedom from. In the days of anarchy, it was freedom to. Now you are being given freedom from. Don't underrate it."