If the shirts are woven, you shouldn't have any problems at all, and don't need stabilizer. If you are concerned, just gently pull the shirt fabric both up and down, then side to side and compare it with pulling quilting cotton the same way. I've done lots of recycled shirt quilts. I look for 100% cotton, but if I need a certain color, or if there is a really wonderful print in a woven blend, I will get it and mix it with cottons, no problem. When repurposing garments, I make sure that any yardage I use with it is pre washed because the garment has been. If the shirts are knits, you would want to stabilize.