A stabilizer on T shirts and sweatshirts as well has handkerchiefs is something that should be used to prevent shifting and stretching. On other cottons you may not need it. I am working on a memory quilt right now that has everything from flannels and almost leathery fabrics to thin wispy fabrics many of these pieces need a stabilizer to even begin placement in the quilt plan. Because of the nature of the quilt all the memories will be on the back of the quilt.
You will have many options to work with, be creative but do stabilize your blocks for the best results.