Wideband and polarization-independent wavelength filters with low sensitivity to temperature variations have great potential for wavelength division multiplexing applications. However, simultaneously achieving these metrics is challenging for silicon-on-insulator photonics technology. Here, we harness the reduced index contrast and the low thermo-optic coefficient of silicon nitride to demonstrate waveguide Bragg grating filters with wideband apolar rejection and low thermal sensitivity. Filter birefringence is reduced by judicious design of a triangularly shaped lateral corrugation. Based on this approach, we demonstrate silicon nitride Bragg filters with a measured polarization-independent 40 dB optical rejection with negligible off-band excess loss, and a sensitivity to thermal variations below 20 pm/°C.