The Fe electronic structure and magnetism in (i) monoclinic Ca$_2$FeReO$_6$ with a metal-insulator transition at $T_{MI} sim 140$ K and (ii) quasi-cubic half-metallic Ba$_2$FeReO$_6$ ceramic double perovskites are probed by soft x-ray absorption spectroscopy (XAS) and magnetic circular dichroism (XMCD). These materials show distinct Fe $L_{2,3}$ XAS and XMCD spectra, which are primarily associated with their different average Fe oxidation states (close to Fe$^{3+}$ for Ca$_2$FeReO$_6$ and intermediate between Fe$^{2+}$ and Fe$^{3+}$ for Ba$_2$FeReO$_6$) despite being related by an isoelectronic (Ca$^{2+}$/Ba$^{2+}$) substitution. For Ca$_2$FeReO$_6$, the powder-averaged Fe spin moment along the field direction ($B = 5$ T), as probed by the XMCD experiment, is strongly reduced in comparison with the spontaneous Fe moment previously obtained by neutron diffraction, consistent with a scenario where the magnetic moments are constrained to remain within an easy plane. For $B=1$ T, the unsaturated XMCD signal is reduced below $T_{MI}$ consistent with a magnetic transition to an easy-axis state that further reduces the powder-averaged magnetization in the field direction. For Ba$_2$FeReO$_6$, the field-aligned Fe spins are larger than for Ca$_2$FeReO$_6$ ($B=5$ T) and the temperature dependence of the Fe magnetic moment is consistent with the magnetic ordering transition at $T_C^{Ba} = 305$ K. Our results illustrate the dramatic influence of the specific spin-orbital configuration of Re $5d$ electrons on the Fe $3d$ local magnetism of these Fe/Re double perovskites.
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