Protein crystallization experiments at reduced gravity have yielded crystals that, depending on the specific material, are either superior or inferior in their structural perfection compared to counterparts grown at normal gravity. A reduction of the crystals' quality due to their growth at low gravity cannot be understood from existing models. Our experimental investigations of the ground-based crystallization of the protein lysozyme have revealed pronounced unsteady growth layer dynamics and associated defect formation under steady external conditions. Through scaling analysis and numerical simulations we show that the observed fluctuations originate from the coupling of bulk transport with non-linear interface kinetics under mixed kinetics-transport control of the growth rate. The amplitude of the fluctuations is smallest when either transport or interfacial kinetics dominate the control of the crystallization process. Thus, depending on the specific system, crystal quality may be improved by either enhancing or suppressing the transport in the solution. These considerations provide, for the first time, a material-dependent rationale for the advantages, as well as the disadvantages, of reduced gravity for (protein) crystallization.