MnF₂ is widely regarded as a candidate altermagnet, but the magnitude and implications of its altermagnetic band splitting remain debated. Using electronic-structure calculations, we construct minimal models that capture the magnetic and electronic properties of MnF₂. These models show that the parameters governing the chiral magnon splitting and the spin splitting of the electronic bands are relatively small. Moreover, the electronic system lies in the strong-coupling regime, where most magnetic properties are controlled by the ratio t/U between the characteristic hopping amplitude t and the large on-site Coulomb repulsion U. Consequently, all exchange interactions scale as 1/U, so a small altermagnetic hopping δ t produces only a proportionally small exchange term. Upon doping, the altermagnetic contribution to the anomalous Hall effect is likewise suppressed, being smaller than the conventional (non-altermagnetic) contribution by a factor of order δ t/U. In contrast, the behavior of the conductivity tensor σ̂(ω) at ℏ ω ∼ U differs qualitatively, because δ t enters the energies of interband optical transitions directly rather than through the reduced ratio δ t/U. This contribution strongly reshapes σ̂(ω), leading to a dramatic enhancement of the magneto-optical response.