Quantum identity authentication serves as a crucial technology for secure quantum communication, but its security often faces challenges due to quantum hacking of measurement devices. This study introduces a measurement-device-independent mutual quantum identity authentication (MDI MQIA) scheme capable of ensuring secure user authentication, despite the use of measurement devices vulnerable to quantum hacking. To realize the MDI MQIA scheme, we proposed and applied a modified Bell state measurement based on linear optics, enabling the probabilistic measurement of all Bell states. Furthermore, the proposed experimental setup adopted a plug-and-play architecture, thus efficiently establishing the indistinguishability of two photons prepared by the communication members. Finally, we successfully performed a proof-of-principle experimental demonstration of the proposed scheme using a field-deployed fiber, achieving quantum bit error rates of less than 3%.