I have no issues quilting over the screen printed t-shirts on my longarm. I use a size 18 needle, stitch length of 12 and Omni thread with magna glide bobbins. I always do a free motion a edge to edge with a simple large meander and never use dense quilting. If there are shirts with plastic type graphics I quilt around these close to the logo but not over the plastic. I also discourage the use of these plastic type shirts to the ladies I know that make t-shirt quilts. I linked a good video of Lisa Capen quilting a t-shirt quilt, she makes and quilts lots of them. I love all her videos, she is a great teacher.
https://www.youtube.com/watch?v=w72E8qdFMqs&t=1s