Well, is is very difficult to be sure from a photo. Having it in hand makes it easy. I think your hat is a coated natural straw braid, but again would need a closer examination to be sure. If you can scrape a little bit of the surface in an unseen place or take a snippet it will give clues.
As far as synthetics being used in fashions, the term synthetic can be subjective. Rayon is made from plants (cellulose) , a natural source, but is not always considered a natural fiber, to some people it is a natural fiber and to others it is a synthetic. My opinion falls somewhere in between. A synthetic made from natural substances. Anyway.....
Synthetics straw braids for hats have been in use as far back as the Edwardian era. There are a number of materials used and trade names applied to these straws. In the antique hats they used what was called Pyroxylin straw or "crin" (crinoline) and other types which were usually cellulose based (cello). Synthetic straws were made of cellulose, toxic chemicals, paper, paints, or a mix of those materials. Often natural straws were treated, mixed with these materials or straw was coated with lacquer, etc. Companies who made some of these synthetics closely guarded their recipes so we do not often know exactly what is in there. Most were made in Europe so during WWII we tend to see more of the coated natural straws. But synthetics were still around then also.
And natural straws were coated to add color, sheen and stiffness, especially if the straw was very narrow. Natural Milan straw has a wonderful sturdy feel and stiffness even if very narrow, and cheaper straw were often softer so they added a coating to give them more firmness to keep the hat's shape.
After WWII yes we see more plastic based materials used (nylons, etc), especially the straws coming from Switzerland and Italy.
Too much information, I know.
Sorry I cannot be sure on your hat, but would know if I had it in hand.
