Despite its radical assumption of ecological equivalence between species, neutral biodiversity theory can often provide good fits to species abundance distributions observed in nature. Major criticisms of neutral theory have focused on interspecific differences, which are in conflict with ecological equivalence. However, individual-level neutrality in nature is also broken by differences between conspecific individuals at different life stages, which in many communities may vastly exceed interspecific differences between individuals at similar stages. These individual-level asymmetries have not been fully explored in species-neutral models, and it is not known whether demographic stage structure affects macroecological patterns in neutral theory. Here we present a two-stage neutral model, where both fecundity and mortality are allowed to change as an individual moves from a stage to the other. We explore qualitatively different scenarios, and compare numerically obtained species abundance distributions to the predictions of unstructured neutral theory. We find that abundance distributions are robust to this kind of stage structure, but only so long as subpopulations at different stages fluctuate in synchrony. On the other hand, species abundance distributions can differ significantly from the unstructured case if adults have sufficiently low fecundity and mortality. In addition, we show that the cumulative number of births per species, which is distributed as a power law with a 3/2 exponent, is invariant even when the SAD departs from unstructured model predictions. Our findings potentially explain power law-like abundance distributions in systems with strong demographic structure, such as eusocial insects and human given names, and may partially rehabilitate species abundance distributions from past criticisms as to their inability to distinguish between biological mechanisms.