We investigated the reproducibility of FairCLIP, proposed by Luo et al. (2024), for improving the group fairness of CLIP (Radford et al., 2021) by minimizing image-text similarity score disparities across sensitive groups using the Sinkhorn distance. The experimental setup of Luo et al. (2024) was reproduced to primarily investigate the research findings for FairCLIP. The model description by Luo et al. (2024) was found to differ from the original implementation. Therefore, a new implementation, A-FairCLIP, is introduced to examine specific design choices. Furthermore, FairCLIP+ is proposed to extend the FairCLIP objective to include multiple attributes. Additionally, the impact of the distance minimization on FairCLIP's fairness and performance was explored. In alignment with the original authors, CLIP was found to be biased towards certain demographics when applied to zero-shot glaucoma classification using medical scans and clinical notes from the Harvard-FairVLMed dataset. However, the experimental results on two datasets do not support their claim that FairCLIP improves the performance and fairness of CLIP. Although the regularization objective reduces Sinkhorn distances, both the official implementation and the aligned implementation, A-FairCLIP, were not found to improve performance nor fairness in zero-shot glaucoma classification.