Applications of the Digital Sharing Economy (DSE), such as Uber, Airbnb, and TaskRabbit, have become a main facilitator of economic growth and shared prosperity in modern-day societies. However, recent research has revealed that the participation of minority groups in DSE activities is often hindered by different forms of bias and discrimination. Evidence of such behavior has been documented across almost all domains of DSE, including ridesharing, lodging, and freelancing. However, little is known about the underlying design decisions of DSE platforms which allow certain demographics of the market to gain unfair advantage over others. To bridge this knowledge gap, in this paper, we systematically synthesize evidence from 58 interdisciplinary studies to identify the pervasive discrimination concerns affecting DSE platforms along with their triggering features and mitigation strategies. Our objective is to consolidate such interdisciplinary evidence from a software design point of view. Our results show that existing evidence is mainly geared towards documenting and mitigating issues of racism and sexism affecting platforms of ridesharing, lodging, and freelancing. Our review further shows that discrimination concerns in the DSE market are commonly enabled by features of user profiles and commonly impact reputation systems.