As Large Language Models (LLMs) are deployed across diverse regions, aligning them with pluralistic cultures is crucial for improving user engagement and mitigating cultural conflicts. Recent work has curated, either synthesized or manually annotated, culture-specific corpora for alignment. Nevertheless, inspired by cultural theories, we recognize they face two key challenges. (1) Representativeness: These corpora inadequately capture the target culture's core characteristics, causing insufficient cultural coverage and redundancy; (2) Distinctiveness: They fail to distinguish the unique nuances of the target culture from patterns shared across relevant ones, hindering precise culture modeling. To handle these challenges, we introduce CAReDiO, a novel data optimization framework that alternately optimizes culture-sensitive questions and responses according to two information-theoretic objectives in an in-context manner, enhancing both cultural representativeness and distinctiveness of constructed data. Extensive experiments on 15 cultures demonstrate that CAReDiO can create high-quality data with richer cultural information and enable efficient alignment of small open-source or large proprietary LLMs with as few as 200 training samples, consistently outperforming previous datasets in both multi-choice and open-ended benchmarks.