Strong Fermi-level pinning (FLP) always occurs at the two-dimensional (2D) semiconductor-metal interface due to the complex interfacial charge transfer. By using monolayer (ML) Bi₂OS₂, an emerging 2D semiconductor with the highest electron mobility, the Schottky barrier heights (SBHs) and origin of charge transfer at Bi₂OS₂-metal interfaces are systematically studied based on density functional theory calculations. In 3D metal-Bi₂OS₂ interfaces, the formation of chemical bonding and the effect of Pauli exchange repulsion are found to be responsible for the strong interfacial charge transfer, resulting in strong FLP, and the direction of charge transfer induced by the two factors is opposite. Besides, an extra interfacial charge transfer is expected to equilibrate the Fermi level when the work functions (WFs) of metal electrodes are out of the range of electron affinity energy and ionization energy of semiconductors. For 2D metal-ML Bi₂OS₂ interfaces, surprisingly, the FLP is found to be entirely suppressed, and thereby, the 2D metal-Bi₂OS₂ contacts obey the conventional Schottky-Mott model. Such intriguing behavior arises from the 2D metal electrodes chosen in this work can effectively shield the effect of Pauli exchange repulsion. Consequently, wide-range and linear-tunable SBHs can be obtained and the conversion from n-type Ohmic contact to p-type Ohmic contact can be achieved by using 2D metal electrodes with different WFs. This study not only provides a theoretical foundation for selecting favorable metal electrodes in devices based on ML Bi₂OS₂, but also helps to enhance the understanding of the mechanism of interface interaction between metals and 2D semiconductors.