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In this project, we have developed and studied a deep neural network-based individual-agnostic general-purpose binaural localizer (BL) for sound sources located at arbitrary directions on the $4\pi$ sphere. Unlike binaural localization models trained with an HRIR catalog associated with a specific head and ear shape, an individual-agnostic model aims for the generalization over the individuality of HRIRs, and does not assume a-priori knowledge about the HRIRs which the sound wave is filtered through at recording time. The proposed model was evaluated via localization tests using public binaural room impulse responses (BRIRs) and binaural recording datasets and was found to deliver more robust and accurate localization in noisy and reverberant conditions and unknown recording-time HRIRs compared to BLs trained on a single subject's HRIR catalog. The proposed model is also designed to support multiple or moving sources, and demonstrations for these scenarios are provided.