Thin brass sometimes will break after time goes by, due to the amount of pressure strain put on the eyelet. Eyelets can also be purchased which are thicker than others normally used, to help avoid the cracking.
Plastic is a generic term for so many different materials that it is difficult to answer.
I have used Delrin for a backup for harp strings made both of nylon and of metal wound strings. Sometimes I have used a larger than the hole rod of Delrin and drilled a hole through the center. In both cases I've purchased several sizes of Delrin rod and adjusted as one would adjust when using different sizes of eyelets. Some plastics might be too brittle and crack, or be soft, not enough strength to prevent the string from digging into the plastic. Installation of eyelets is easy, be sure to try a few in a sample piece of wood of the same material as the string rib or soundboard, so the hole drilled will not be too small or too large.