Silicon carbide (SiC), having various intrinsic color centers, is a highly promising optical materials for making monolithic quantum integrated photonic circuits, by combining the single-photon sources with the integrated photonic components in SiC integrated platforms. Based on this quantum-material platform, we propose polarization-independent 1 × 2 and 2 × 2 multimode interference based beam splitters and Mach-Zehnder interferometers (MZI) for single-photon manipulation with unknown polarization states. We experimentally demonstrate that these devices exhibit excellent performances with incident light at both high power (>-10 dBm) and ultra-low power (<-100 dBm). The 1 × 2 and 2 × 2 beam splitters have low average loss of 1 dB and 1.5 dB, with a wide bandwidth of >100 nm and >70 nm, respectively. The MZI exhibits high transmittance, with a visibility of 98.3% and 97.6% for the high-power measurement and an even higher visibility of 99.0 ± 0.4% and 98.7 ± 0.6% for the ultra-low power measurement, for the TE and TM polarizations, respectively.