Large Language Models (LLMs) have shown remarkable performance across various applications, but their deployment in sensitive domains raises significant concerns. To mitigate these risks, numerous defense strategies have been proposed. However, most existing studies assess these defenses in isolation, overlooking their broader impacts across other risk dimensions. In this work, we take the first step in investigating unintended interactions caused by defenses in LLMs, focusing on the complex interplay between safety, fairness, and privacy. Specifically, we propose CrossRiskEval, a comprehensive evaluation framework to assess whether deploying a defense targeting one risk inadvertently affects others. Through extensive empirical studies on 14 defense-deployed LLMs, covering 12 distinct defense strategies, we reveal several alarming side effects: 1) safety defenses may suppress direct responses to sensitive queries related to bias or privacy, yet still amplify indirect privacy leakage or biased outputs; 2) fairness defenses increase the risk of misuse and privacy leakage; 3) privacy defenses often impair safety and exacerbate bias. We further conduct a fine-grained neuron-level analysis to uncover the underlying mechanisms of these phenomena. Our analysis reveals the existence of conflict-entangled neurons in LLMs that exhibit opposing sensitivities across multiple risk dimensions. Further trend consistency analysis at both task and neuron levels confirms that these neurons play a key role in mediating the emergence of unintended behaviors following defense deployment. We call for a paradigm shift in LLM risk evaluation, toward holistic, interaction-aware assessment of defense strategies.