Quantization is widely adopted to reduce the computational cost of large language models (LLMs); however, its implications for fairness and safety, particularly in dynamic quantization and multilingual contexts, remain underexplored. In this work, we conduct a systematic study of how static and dynamic quantization methods impact fairness and safety across benchmarks measuring intrinsic and extrinsic bias and safety alignment. For fairness, we evaluate English, French, Dutch, Spanish, and Turkish; for safety, we focus on English, Korean, and Arabic. Our findings reveal that quantization consistently degrades fairness and safety, with dynamic methods demonstrating greater stability than static ones. Moreover, fairness degradation varies across languages, while safety deterioration is especially pronounced in non-English settings. To address these risks, we introduce Critical Weight Protection, a novel technique that identifies and preserves fairness- and safety-critical weights during quantization. This approach effectively mitigates bias and safety deterioration without costly retraining or alignment, maintaining trustworthiness while retaining efficiency.