I've never had an issue with any type of thread ( with the possible exception of invisible ) cutting fabric.
I have however had issues from time to time of thread breaking before the fabric wore out. This has mainly been an issue in clothing which gets much rougher usage than most quilts.
I do pay attention to the quality of the thread I purchase whether it be cotton, poly/cotton or all poly. There can be a visible difference in some threads - lots of loose fibers, which to my mind equals lots of lint in my machine.