I really think it's a matter of personal preference these days.
I have tested my polyester bobbin thread under my hot Rowenta iron and it does not melt or change at all. The Superior website says that polyester threads tolerate less heat than cotton threads but, for me, heat is not an issue for me with this particular thread. For anyone contemplating using polyester thread for piecing, I do recommend testing it with a hot iron before using. There may be polyester threads that do melt under a hot iron.
Regarding invisible nylon thread, the "fishing line" pokies from commercial comforters should not be compared to the YLI nylon monofilament thread that Harriet Hargrave has always recommended. I have used the YLI for years, and a strand is as fine as a baby's hair. I personally don't like it for quilting as I preferring my thread to show; also, for the close quilting I like to do, polyester or cotton thread is softer.