Here's a little backing humor:
Two cities in our valley were founded by Englishmen. Early settlers to our region included English, Irish, Wales, Switzerland, Alsace (sometimes Germany, sometimes France), some areas of Germany, and Bohemia/Czechoslovakia (as in Moravians who founded our valley's city of Bethlehem and moved to Germany to escape religious persecution before coming here).
In the mid-19th century, Pennsylvania Germans learned quilting from their "English" neighbors. I've read that after one generation, weaving was abandoned all together for quilts.
So getting back to those muslin backings....
Another quilt in my collection, similar to the one above also has a muslin backing:
It is possible, possibly probable, that muslin was used on the back of these two later quilts simply to save money for whatever causes either of these quilts were meant to support.