It has been a long held belief that cotton quilts should have cotton thread. Some of the discussions have become quite heated at times as there are still many that hold this belief. I think our fabrics have changed over time and it really isn't that big of a deal anymore, but we all have our own preferences.
Longarm machines really do have their own personalities. I know this sounds strange, but there are machines that run much more easily on cotton thread. My machine really likes polyester thread and I do not have to fiddle with the tension nearly as much. Cotton thread requires a lot more tension changes for me. Another person's machine may be totally opposite.
I use what people who want a quilt quilted prefer. I have several quilts that my mom had long arm quilted many years ago, that show no sign of stress from the polyester. I also have a quilt that she SID with a regular sewing thread from town that also has no problems. The fabric is going to wear out before the thread ever does. I also have a Dresden that was quilted with monofilament thread. I hate that quilting thread and will probably end up taking it out and redoing it sometime.
So what it really amounts to for me is, use what you feel comfortable with.