While there are threads I will not use with cottons, the modern threads like So Fine were designed with cotton in mind.
When I started quilting, way back before there were rotary cutters, there were still quilt police. The going adage was "cotton only" but I was very happy with Dual Duty, which was cotton wrapped poly. We weren't all that sure about storing fabric in plastic containers or bags either, but after 50 years I'm no longer so worried about that either...
I can tell you my early quilts from the 70s went through a lot of hard use and machine washing, and the Dual Duty thread was never a problem. The problem was I didn't quilt closely enough and the unquilted areas rotted away, leaving the seams and the in the ditch quilting strongly holding together the threads.