Without wishing to be accused of "showing off" again on GN, I am a bit of an expert on this as we used to buy 10 or so new parasols each year! I liked to have different plain colours to give an individual feel to each area they were put in. In terms of fading, the blue and red ones were the worst, green not so bad. The beige/cream ones obviously didn't fade at all. I like them best and always think of tropical beaches.
As J52 says, in terms of sun protection it is the quality and thickness of the canvas or cotton that really matters. It's a bit like thread counts on sheets.
Polyester is not a good insulator and the parasols can get very hot when it is warm. Strangely they also get very cold too! When you feel the fabrics check also that too much teflon coating hasn't been applied because it isn't breathable and this can lead to condensation building up inside. This can cause mould. Always put the parasols down after use each night, except if it has rained and they are wet.
I also used to stitch my own awning for the gazebo and used a wide stripe material in dark green and cream which worked really well for shade.