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Magnetic Josephson junctions (MJJs) are a special class of hybrid systems where antagonistic correlations coexist, thus providing a key for advances in weak superconductivity, superconducting spintronics, and quantum computation. So far, the memory properties of MJJs have been mostly investigated in view of digital electronics and for spintronic devices at liquid-helium temperature. At the operating temperature of quantum circuits, a magnetic order can rise in a superconductor (S) at the S/ferromagnet (F) interface, i.e., the inverse proximity effect (IPE), thus leading to a significant modification of the magnetic field patterns in MJJs. In this work, we have carried out a comparative investigation of the magnetic behavior of tunnel MJJs with a strong ferromagnetic layer inserted in the layout of both Nb and Al JJs, respectively. The comparative analysis validates the crucial role of the temperature, the fundamental scaling energies of S/F coupling systems, and the transparency of the S/F interface. This investigation points out that the IPE is a key aspect to consider when designing tunnel MJJs operating well below 4 K and thus in the perspective of hybrid superconducting quantum architectures. [ABSTRACT FROM AUTHOR]