Concepts of Mobility-on-Demand (MOD) and Mobility as a Service (MaaS), which feature the integration of various shared-use mobility options, have gained widespread popularity in recent years. While these concepts promise great benefits to travelers, their heavy reliance on technology raises equity concerns as socially disadvantaged population groups can be left out in an era of on-demand mobility. This paper investigates the potential uptake of MOD transit services (integrated fixed-route and on-demand services) among travelers living in low-income communities. Specially, we analyze people's latent attitude towards three shared-use mobility services, including ride-hailing services, fixed-route transit, and MOD transit. We conduct a latent class cluster analysis of 825 survey respondents sampled from low-income neighborhoods in Detroit and Ypsilanti, Michigan. We identified three latent segments: shared-mode enthusiast, shared-mode opponent, and fixed-route transit loyalist. People from the shared-mode enthusiast segment often use ride-hailing services and live in areas with poor transit access, and they are likely to be the early adopters of MOD transit services. The shared-mode opponent segment mainly includes vehicle owners who lack interests in shared mobility options. The fixed-route transit loyalist segment includes a considerable share of low-income individuals who face technological barriers to use the MOD transit. We also find that males, college graduates, car owners, people with a mobile data plan, and people living in poor-transit-access areas have a higher level of preferences for MOD transit services. We conclude with policy recommendations for developing more accessible and equitable MOD transit services.