The COVID-19 pandemic has accelerated the development and adoption of wastewater-based epidemiology. Wastewater samples can provide genomic information for detecting and assessing the spread of SARS-CoV-2 variants in communities and for estimating important epidemiological parameters such as the selection advantage of a viral variant. However, despite demonstrated successes, epidemiological data derived from wastewater suffers from potential biases. Of particular concern are shedding profiles, which can affect the relationship between true viral incidence and viral loads in wastewater. Changes in shedding between variants may decouple the established relationship between wastewater loads and clinical test data. Using mathematical modeling, simulations, and Swiss surveillance data, we demonstrate that estimates of the selection advantage of a variant are not biased by shedding profiles. We show that they are robust to differences in shedding between variants under a wide range of assumptions, and identify specific conditions under which this robustness may break down. Additionally, we demonstrate that differences in shedding only briefly affect estimates of the effective reproduction number. Thus, estimates of selective advantage and reproduction numbers derived from wastewater maintain their advantages over traditional clinical data, even when there are differences in shedding among variants.