Bottom-up fabrication methods are a promising approach for fabrication of three-dimensional photonic structures. These methods are cheap and relatively simple, but they always result in randomized photonic structures. For this reason, we investigate robustness of photonic bandgaps (PBGs) in two-dimensional plasmonic crystals (PlCs) to the four types of disorder: disorder in rod position, disorder in rod radius, disorder in rod cross section, and disorder due to missing rods. We compare behavior of two types of PBGs: Bragg PBGs, which arise due to Bragg reflections, and plasmonic PBGs due to localized surface plasmon resonances for electric field normal to the rods. Bragg PBGs are sensitive to the disorder since they stem from collective reflections within PlCs. On the other hand, the plasmonic PBGs are quite robust to the disorder since they arise from plasmonic resonances in single inclusions and they are not related to any collective phenomena. Therefore, applications of plasmonic PBGs could facilitate wide utilization of photonic bandgap media fabricated by bottom-up fabrication methods.