Birefringence is helpful in controlling polarization evolution inside the fiber. You can use such specialized fibers to build environmentally stable fiber lasers and actually people are working in this area for quite a long time.
Polarization maintaining fibers (PMF) for controlling the polarization state of a light is largely used in fiber sensors, which is based on birefringence developed across the xy- axes of an optical fiber. Now, its PCF counterpart can also be used for the same application. More application of birefringent PCF optical fibers, like conventional birefringent fibers, is used as a polarizer in optical sensing systems. And wherever polarization component of a light is required, it can be used.