Differential privacy (DP) has been in the public spotlight since the announcement of its use in the 2020 U.S. Census. While DP algorithms have substantially improved the confidentiality protections provided to Census respondents, concerns have been raised about the accuracy of the DP-protected Census data. The extent to which the use of DP distorts the ability to draw inferences that drive policy about small-populations, especially marginalized communities, has been of particular concern to researchers and policy makers. After all, inaccurate information about marginalized populations can often engender policies that exacerbate rather than ameliorate social inequities. Consequently, computer science experts have focused on developing mechanisms that help achieve equitable privacy, i.e., mechanisms that mitigate the data distortions introduced by privacy protections to ensure equitable outcomes and benefits for all groups, particularly marginalized groups. Our paper extends the conversation on equitable privacy by highlighting the importance of inclusive communication in ensuring equitable outcomes for all social groups through all the stages of deploying a differentially private system. We conceptualize Equitable DP as the design, communication, and implementation of DP algorithms that ensure equitable outcomes. Thus, in addition to adopting computer scientists' recommendations of incorporating equity parameters within DP algorithms, we suggest that it is critical for an organization to also facilitate inclusive communication throughout the design, development, and implementation stages of a DP algorithm to ensure it has an equitable impact on social groups and does not hinder the redressal of social inequities. To demonstrate the importance of communication for Equitable DP, we undertake a case study of the process through which DP was adopted as the newest disclosure avoidance system for the 2020 U.S. Census. Drawing on the Inclusive Science Communication (ISC) framework, we examine the extent to which the Census Bureau's communication strategies encouraged engagement across the diverse groups of users that employ the decennial Census data for research and policy making. Our analysis provides lessons that can be used by other government organizations interested in incorporating the Equitable DP approach in their data collection practices.