Why do iron(II) ions and chromium have different electronic configurations?
For starters, it isn’t nearly as simple as it is usually put in chemistry classes to explain chromium’s ground state electron configuration.

$\ce{Cr(0)}$ and $\ce{Fe(II)}$ have the same number of valence electrons. You might have heard of the concept of isolobality, which, briefly explained, suggests that compounds with similar electronic configurations (isolobal configurations) will react similarly; so you could replace $\ce{F}$ with $\ce{OMe}$ or even $\ce{[Co(CO)4]}$. The concept has its values and its strong simplifications which I will not go into here.

However, even assuming the isolobality concept’s validity, it would not count $\ce{Cr(0)}$ and $\ce{Fe(II)}$ as isolobal to each other. The reasoning is rather simple: One is a neutral metal, the other is a cation with $+2$ charge. For every electron an atom looses, the atom’s orbitals will contract and the atomic (or ionic) radius will decrease. This also changes the energy levels between orbitals and will affect lower d-orbitals differently than higher s-orbitals.

The result is that the $\ce{4s}$ and $\ce{3d}$ orbitals are now so dissimilar in energy, that electrons hopping back or forth is now no longer an option.