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Photonic parity projection plays an important role in photonic quantum information processing. Nondestructive parity projections normally require high-fidelity controlled- $Z$gates between photonic and matter qubits, which can be experimentally demanding. In this paper, we propose a nearly deterministic parity projection protocol on two photonic qubits which only requires stable matter-photon controlled-phase gates. We also demonstrate that our protocol can tolerate moderate Gaussian phase errors in the controlled-phase gates as well as Pauli errors on the matter qubits. The fact that our protocol does not require perfect controlled- $Z$gates makes it more amenable to experimental implementation. Although we focus on photonic qubits, our protocol can be applied to any physical system or circuit with imperfect controlled- $Z$gates. Our protocol also provides a new optimization space for parity projection operations on various physical platforms, which is potentially beneficial for achieving high-fidelity parity projection operations. Published by the American Physical Society2024