I have 20 year old quilts that I pieced with cotton covered polyester, machine washed and dried about every couple of months and used (abused! ;-) ) every day. The thread is not cutting the fabric. That thread cutting fabric idea is, as they say, a wives tale. Bob at Superior Threads will back this up. I've heard about mythical quilts that were cut by old time 50's polyester thread. I have yet to see them. I have to wonder if they're real.
If you take a modern poly core thread and a 50/3 cotton thread and break each, they will require similar effort to break. They are both medium weight threads, and both good. IMHO, a good thread for piecing is one where you have to wrap it once around your hand to break it. If you can hold both ends without wrapping and can break it, that's a bad sign. People say, no, you can't piece with serger thread because it's too weak. But 50/2 threads like Aurifil are weaker. Just try it.
If you piece with a light weight thread (e.g. Aurifil), IMHO you should quilt closely to protect the seams from breaking. I wish I could remember which high end machine quilter agreed with that sentiment, but at least one did.
A 50/3 thread is the same as about a tex 35. It is considered medium weight. I would be inclined not to go any smaller than that for piecing anything larger than a wall-hanging.
But talking about piecing rather than quilting is a slight high-jacking. Sorry about that.