Chafe can seriously effect the longevity of your synthetic rigging. The best method to avoid the problem is to make sure that no two lines rub past each other.
In situations like the headstay, avoiding chafe is not possible since the sail hanks attach directly to it and will slide, shimmy, and jiggle around; sawing into your headstay and destroying it in no time. To mitigate this, special steps must be taken.
Service (wrapping) the ends of the stay
The headstay itself must be wrapped in a sacrificial covering, the covering will suffer chafe and be replaced before any damage happens to the stay. I recommend using the chafe sleeve by New England Ropes, designed for protecting dyneema. The covering is rather tricky to replace though, requiring the splice at one end to be removed so the old cover can be removed and a new cover installed. To further prolong the life of the chafe sleeve, I also service the ends of the stay with thin dyneema.
This line is 7/64" and wrapped tightly around the stay using a serving mallet. The process is very time consuming, taking around an hour for a few feet of the stay. The service protects the chafe sleeve in the areas of highest wear: the head and the tack. Since these areas will wear out sooner than the rest of the stay, they can simply be unwound and re-serviced without having to undo the splices.
Another method to mitigate chafe is by using soft hanks. I had my sail maker place a nylon webbing that loops over the stay and the bronze hank is located on the side. This keeps the bronze hank from cutting through the fibers when under load, as the soft nylon spreads the loads over a broad area rather than a sharp point load.