Demand-responsive transport (DRT) is an emerging mode of transport. Offering a flexible and affordable service, it bridges the gap between the conventional public transport (PT) and taxis or private cars. While most existing studies focus on optimizing vehicle scheduling and profit, the potential of using DRT to improve public accessibility and reduce mobility inequality is often overlooked. In this study, we develop and implement an accessibility- and equity-oriented DRT operational strategy. Instead of treating travel requests as homogeneous, we introduce heterogeneity into the system. By categorizing passengers into different groups based on their level of accessibility, the DRT feet can be utilized more efficiently, meaning that a substantially smaller feet can be sufficient. The system ensures that all passengers with reduced mobility receive door-to-door mobility services, making travel easier and more convenient for them. In addition, direct DRT connections are provided to passengers with poor PT service, thereby improving their accessibility and reducing overall inequality in mobility supply. To demonstrate the impact and effectiveness of this novel DRT operational strategy, we conduct a case study based on a real-world scenario in Dresden. Results show that the proposed approach substantially improves equity in travel times, reducing normalized travel-time dispersion by nearly 50% compared to the baseline, while achieving significant accessibility gains with a comparatively small feet by prioritizing underserved users rather than serving all requests uniformly.