Beyond-diagonal reconfigurable intelligent surface (BD-RIS) has arisen as a promising technology for enhancing wireless communication systems by enabling flexible and intelligent wave manipulation. This is achieved through the interconnections among the ports of the impedance network, enabling wave reconfiguration when they flow through the surface. Thus, the output wave at one port depends on waves impinging on neighboring ports, allowing non-local control of both phase and magnitude. Non-reciprocal (NR)-BD-RIS further enhances this capability by breaking circuit reciprocity and, consequently, channel reciprocity. In contrast to conventional reciprocal (R)-BD-RIS and diagonal (D)-RIS that are constrained by circuit and channel reciprocity such that they only allow bidirectional communications, i.e., between UE1 and UE2, NR-BD-RIS can additionally enable uni-directional communications, that is, UE1 to UE2 to UE3, hence effectively enabling a wireless circulator. Specifically, this paper introduces a novel application of NR-BD-RIS in full-duplex (FD) wireless circulators, where multiple FD devices communicate via an NR-BD-RIS. This system is particularly beneficial for secure transmission, as it enforces one-way communication among FD devices, suppresses signal from all other users (UE), and thus prevents eavesdropping. In addition, a physics-compliant system model is considered by incorporating structural scattering, also known as specular reflection. By accounting for this effect, the advantages of NR-BD-RIS are further validated. Specifically, we formulate an sum-rate maximization problem and propose an iterative optimization algorithm that employs block coordinate descent (BCD) and penalty dual decomposition (PDD) methods. Numerical evaluations illustrate that NR-BD-RIS outperforms conventional R-BD-RIS and D-RIS in terms of sum-rate and secrecy rate.