Magnetic properties of the substitution series Ru1-xCrxCl3 were investigated to determine the evolution from the anisotropic Kitaev magnet α-RuCl3 with Jeff=1/2 magnetic Ru3+ ions to the isotropic Heisenberg magnet CrCl3 with S=3/2 magnetic Cr3+ ions. Magnetization measurements on single crystals revealed a reversal of the magnetic anisotropy under doping, which we argue to arise from the competition between anisotropic Kitaev and off-diagonal interactions on the Ru-Ru links and approximately isotropic Cr-Ru and isotropic Cr-Cr interactions. In addition, combined magnetization, ac susceptibility, and specific-heat measurements clearly show the destabilization of the long-range magnetic order of α-RuCl3 in favor of a spin-glass state of Ru1-xCrxCl3 for a low doping of x≤0.1. The corresponding freezing temperature as a function of Cr content shows a broad maximum around x ≤ 0.45.