Across academia, government, and industry, data stewards are facing increasing pressure to make datasets more openly accessible for researchers while also protecting the privacy of data subjects. Differential privacy (DP) is one promising way to offer privacy along with open access, but further inquiry is needed into the tensions between DP and data science. In this study, we conduct interviews with 19 data practitioners who are non-experts in DP as they use a DP data analysis prototype to release privacy-preserving statistics about sensitive data, in order to understand perceptions, challenges, and opportunities around using DP. We find that while DP is promising for providing wider access to sensitive datasets, it also introduces challenges into every stage of the data science workflow. We identify ethics and governance questions that arise when socializing data scientists around new privacy constraints and offer suggestions to better integrate DP and data science.