We analyze theoretically the coupling properties of Bragg gratings written in highly birefringent photonic crystal fibers with doped core and show how they can be tuned by the parameters of a microstructured fiber. We apply the coupled mode theory combined with a fully vectorial mode solver based on the plane-wave method. The results indicate large differences in interaction with the grating for the two linearly polarized fundamental modes. We show fiber designs, which provide single-mode operation with high birefringence and at the same time a high coupling efficiency of the grating. Such features can be used in fiber sensors, fiber laser configurations or to introduce a polarization dependent feedback in a long external cavity system with a semiconductor laser.