Personality alignment tailors Large Language Models (LLMs) for personalized interactions. Most existing studies focus on prompting, post- training, or representation steering to elicit trait expression, but they often compromise the general capabilities like reasoning and truthfulness. In this work, we empirically verified the existence of the Personality Alignment Tax (PAT) that distribution shifts and conflicting objectives during personality updates overwrite pre-trained competencies. To mitigate this tax, we propose a Personality-Orthogonal Gradient Projection (POGP) plug-in that preserves the capability in personality alignment. Specifically, POGP estimates the general-capability subspace from capability reference benchmarks and projects personality gradients onto the orthogonal complement before updating. This isolates and neutralizes conflicting gradients while maintaining the pre-trained reasoning capabilities. Experiments on the BIG5-CHAT dataset with two backbone LLMs demonstrate that POGP achieves a stronger personality plasticity and capability stability trade-off than baselines.