Recent initiatives known as Future Internet Architectures (FIAs) seek to redesign the Internet to improve performance, scalability, and security. However, some governments perceive Internet access as a threat to their political standing and engage in widespread network surveillance and censorship. In this paper, we provide an in-depth analysis of the design principles of prominent FIAs in terms of their packet structure, addressing and naming schemes, and routing protocols to foster discussion on how these new systems interact with censorship and surveillance apparatuses. Further, we assess the extent to which existing surveillance and censorship mechanisms can successfully target FIA users while discussing privacy enhancing technologies to counter these mechanisms. We conclude by providing guidelines for future research into novel FIA-based privacy-enhancing technologies, and recommendations to guide the evaluation of these technologies.