We report on the anisotropy of the London penetration depth of CaKFe4As4, discussing how it relates to its electronic structure and how it modifies under introduction of disorder, both chemically induced (by Ni substitution) and irradiation induced (by 3.5-MeV protons). Indeed, CaKFe4As4 is particularly suitable for the study of fundamental superconducting properties due to its stoichiometric composition, exhibiting clean-limit behavior in the pristine samples and having a fairly high critical temperature, Tc≈35 K. The London penetration depth λL is measured with a microwave-coplanar-resonator technique that allows us to deconvolve the anisotropic contributions λL,ab and λL,c and obtain the anisotropy parameter γλ=λL,c/λL,ab. The γλ(T) found for the undoped pristine sample is in good agreement with previous literature and is here compared to ab initio density-functional-theory and Eliashberg calculations. The dependence of γλ(T) on both chemical and irradiation-induced disorder is discussed to highlight which method is more suitable to decrease the direction dependence of the electromagnetic properties while maintaining a high critical temperature. Lastly, the relevance of an intrinsic anisotropy such as γλ on application-related anisotropic parameters (critical current, pinning) is discussed in light of the recent employment of CaKFe4As4 in the production of wires.