We propose a novel approach for limiting possible sexual harassment during taxi rides, where penalizing harassing drivers and matching them to passengers play key roles. In this paper, we focus on the matching part. In particular, we propose a novel two-sided market model, with drivers on one side and passengers on another side, where drivers have (1) safety preferences, (2) profit preferences, and (3) gender preferences, for passengers, and passengers have (1) safety preferences, (2) delay preferences, and (3) gender preferences, for drivers. Given these three-layer preferences, we study increasing the safety and stability in matchings, thus possibly reducing the chance of sexual harassment. In addition, we combine safety and stability with maximizing total profit or minimizing total delay. We design a number of algorithms throughout the paper and measure their safety, stability, and efficiency.