Spintronics has been garnering great success in resolving the shortcomings of conventional charge-based electronics and von-Neumann architecture by offering novel computational paradigms almost devoid of leakage effects and volatility issues of traditional CMOS systems. Especially, hybrid CMOS/MTJ circuits integrating all benefits of spintronics with well-evolved CMOS technology have been extensively investigated as candidates for building next-generation processors. Motivated by the importance of magnetic processors, in this work, a novel fully non-volatile reconfigurable magnetic arithmetic logic unit (NVR-MALU) based on majority logic has been proposed. This paper encompasses the prospects of NVRMALU at both the architecture level and circuit level by discussing multi-context hybrid CMOS/MTJ LIM architecture and operation of the circuit. Furthermore, the simulation results of the proposed fully non-volatile reconfigurable magnetic full adder (NVRMFA) making up NVRMALU reveal a remarkable total power reduction by around six to forty-seven folds compared to its contemporary magnetic full adders (MFAs) discussed here. Also, NVRMALU is superior to double pass transistor clocked CMOS (DPTLCMOS) ALU in terms of power reduction by six times, thus qualifying it as an excellent normally OFF, Instant ON digital system. A four-bit extension of NVRMALU has been presented as a sign of the feasibility of the design for multi-bit applications. The transient analysis demonstrates nonvolatile and dynamic reconfigurable traits of NVRMALU in addition to functionality verification. Additionally, variability analysis has been performed to study the factors controlling read and write performances of hybrid circuits from a device-level perspective.