The three quilts that I have used for over 15 years were sewn with cotton covered polyester Dual Duty thread - did not even know some of the brands listed existed at that time -
These quilts have been machine washed and dried - the bias cut bindings are very frayed - however - there has been absolutely no - none - "cutting of the fabric" from the threads on any of the stitching lines.
Two of the quilts were "stitched in the ditch" with additional straight line quilting and one was hand quilted. Again, no "cutting" or damage to the fabric at or near the stitching. ( I think using 20+ stitches to the inch when ditch stitching would/could be damaging - but I probably used 8-10 stitches per inch when quilting "in the ditch")
My experience with the "old" cotton covered polyester Coats & Clark Dual Duty thread has been very positive. There may be better ones available, but i see no reason to not use that thread if you happen to have a lot of it on hand.
I do recommend checking "any" thread for strength - once in a while one gets a "dud" that should not be used - or it may have been improperly stored and gotten weak and will break easily.