This paper explores the coexistence possibilities of Central Bank Digital Currencies (CBDCs) and blockchain-based cryptocurrencies within a post-quantum computing landscape. It examines the implications of emerging quantum algorithms and cryptographic techniques such as Multi-Party Computation (MPC) and Oblivious Transfer (OT). While exploring how CBDCs and cryptocurrencies might integrate defenses like post-quantum cryptography, it highlights the substantial hurdles in transitioning legacy systems and fostering widespread adoption of new standards. The paper includes comprehensive evaluations of CBDCs in a quantum context. It also features comparisons to alternative cryptocurrency models. Additionally, the paper provides insightful analyses of pertinent quantum methodologies. Examinations of interfaces between these methods and blockchain architectures are also included. The paper carries out considered appraisals of quantum threats and their relevance for cryptocurrency schemes. Furthermore, it features discussions of the influence of anticipated advances in quantum computing on algorithms and their applications. The paper renders the judicious conclusion that long-term coexistence is viable provided challenges are constructively addressed through ongoing collaborative efforts to validate solutions and guide evolving policies.