Why and how is the handmaid's tale a realist text set in a fantasy world?

Realist text?
The major realist issues I see in that filthy book is the presence and manipulation of power, the control of sexual activities (, etc), and the role of an individual vs society (or state).

Oh yes, you might want to add right wing religious zealots to your list of reality mirrored in the book. Whether even that is reality in real life or not is arguable. I don't think so, but others have different opinions.

Good luck to you.

http://en.wikipedia.org/wiki/The_Handmaid's_Tale

The term "realist" is going to be up to you to explain, based on your reading and on what you see in the world around you.

=)