The information about polyester being stronger than cotton and therefore cutting through cotton fabric is no longer true. When poly thread was first introduced in the marketplace, it was stronger than cotton thread. Nowadays, however, most of it has similar tensile strength to cotton thread.
You can test thread yourself by snapping it between two hands to see how it breaks. When I tried this, I was very surprised to find that the poly thread actually broke easier than the cotton thread.
I do like the stronger tensile properties of some polyester threads for use in my midarm frame setup; it greatly reduces problems with shredding and thread breakage due to high speed sewing. This is why I prefer Glide thread to King Tut when frame quilting. Plus polyester thread creates much less lint than most cotton threads in my machine.