Today's Internet is experiencing a massive number of users with a continuously increasing need for data, which is the leading cause of introduced limitations among security and privacy issues. To overcome these limitations, a shift from host-centric to data-centric is proposed, and in this context, Information-Centric Networking (ICN) represents a promising solution. Nevertheless, unsettling the current Internet's network layer -i.e., Internet Protocol (IP) -with ICN is a challenging, expensive task since it requires worldwide coordination among Internet Service Providers (ISPs), backbone, and Autonomous Services (AS). Therefore, researchers foresee that the replacement process of the current Internet will transition through the coexistence of IP and ICN. In this perspective, novel architectures combine IP and ICN protocols. However, only a few of the proposed architectures place the security-by-design feature. Therefore, this article provides the first comprehensive Security and Privacy (SP) analysis of the state-of-the-art IP-ICN coexistence architectures by horizontally comparing the SP features among three deployment approaches -i.e., overlay, underlay, and hybrid -and vertically comparing among the ten considered SP features. Lastly, the article sheds light on the open issues and possible future directions for IP-ICN coexistence. Our analysis shows that most architectures fail to provide several SP features, including data and traffic flow confidentiality, availability, and anonymity of communication. Thus, this article shows the secure combination of current and future protocol stacks during the coexistence phase that the Internet will definitely walk across.