Polyesters and cotton fade differently. You can certainly mix them in a quilt. Just be aware that down the line (could be years later) the polyesters will retain their color whereas the cottons will fade. Most vintage quilts are all cotton, and the fabrics gently fade together so the result is a very soft overall look. One that has polyester in it will have patches of the original, bright colors.
I think the meaning of "broadcloth" may have changed over the years. When I look at colored solids for quilts (Moda Bella and Kona), they all seem to say they are "broadcloth". The white and off-white solids usually don't say they are broadcloth, and none of the print cotton fabrics say they are broadcloth either. I have Kona solid-colored navy and black on hand, both of which are "broadcloth" in their online descriptions, and they have a much meatier hand than my regular quilting cottons. My Kona snow, on the other hand, seems to be simply a high quality muslin. The Moda Bella solids I have gotten seem to have a hand similar to my other quilting cottons, but I think they are also described as "broadcloth". Very confusing.