I saw a demo at our guild's winter retreat. The woman who made the T-shirt quilt did not use any interfacing in her quilt since her whole top was made of T-shirts. She used the plain backs of a variety of T-shirts for any fillers she needed. She uses her longarm to quilt these T-shirt quilts and her back was of a different material.
Here's her trick. She sews a temporary border of cotton fabric to the T-shirt top. This keeps the top square and will not stretch as she puts it one her longarm. When the quilting is complete she takes off the border and often saves it for her next t-shirt quilt.