The spin-polarized electronic structure of iron octaethylporphyrin (FeOEP) molecules adsorbed on a pristine and on a $c$($2\times 2$) oxygen-reconstructed Co(100) surface has been analyzed by means of spin-polarized photoemission spectroscopy (SPPES) and first-principles density functional theory with the on-site Coulomb repulsion $U$ term ($\mathrm{DFT}+U$) calculations with and without Van der Waals corrections. The aim is to examine the magnetic exchange mechanism between the FeOEP molecules and the Co(100) substrate in the presence or absence of the oxygen mediator. The results demonstrate that the magnetic coupling from the ferromagnetic substrate to the adsorbed FeOEP molecules is ferromagnetic, whereas, the coupling is antiferromagnetic for the FeOEP on the $c$($2\times 2$)O/Co(100) system. Spin-resolved partial densities of states extracted from ab initio $\mathrm{DFT}+U$ modeling are in fairly good comparison with the electronic spectral densities seen in angle-integrated SPPES energy dispersion curves for submonolayer coverages of FeOEP. Through combined analysis of these spectra and theoretical results, we determine that hybridization of 2$p$ orbitals of N and O with Co 3$d$ orbitals facilitates indirect magnetic exchange interactions between Fe and Co, whereas, a direct Fe-Co interaction involving the Fe $d_{z^2}$ orbital is also found for FeOEP on Co. It is observed through SPPES that the spin polarization of the photoemission-visible molecular overlayers decreases to zero as coverage is increased beyond the submonolayer regime, indicating that only interfacial magnetic coupling is at work. Microspot low-energy electron diffraction and low-energy electron microscopy were performed to characterize the physical order of the molecular coverage, revealing that FeOEP structural domains are orders of magnitude greater in size on $c$($2\times 2$)O/Co(100) than on clean Co(100), which coincides with reduced scattering from the disorder and sharper features seen in SPPES.