In a highly globalized world, it is important for multi-modal large language models (MLLMs) to recognize and respond correctly to mixed-cultural inputs. For example, a model should correctly identify kimchi (Korean food) in an image both when an Asian woman is eating it, as well as an African man is eating it. However, current MLLMs show an over-reliance on the visual features of the person, leading to misclassification of the entities. To examine the robustness of MLLMs to different ethnicity, we introduce MixCuBe, a cross-cultural bias benchmark, and study elements from five countries and four ethnicities. Our findings reveal that MLLMs achieve both higher accuracy and lower sensitivity to such perturbation for high-resource cultures, but not for low-resource cultures. GPT-4o, the best-performing model overall, shows up to 58% difference in accuracy between the original and perturbed cultural settings in low-resource cultures. Our dataset is publicly available at: https://huggingface.co/datasets/kyawyethu/MixCuBe.