Cotton/poly pilling? I have never seen a woven cotton poly shirt that has pills on it.
As with most things, there are nice cotton poly blends - and not so nice one's. Iusually use steam when i press, so there is a bit more wiggle room temperature eize than when using a dry iron.
It is always a good idea to do a burn test on fabrics with unknown fiber content. I forgot to do that and put a dry iron in the middle of a strap I was making for a bag. The fabric was not 100% cotton!
I used the cotton covered polyester (coats & clark) on quilts that I made 20 years ago and see no evidence of the thread cutting the fabric. The bindings are fraying on the edges, but that is from use - not the thread i used.