All eyes are turned towards genomic data and models as the source of knowledge about whether human races exist or not. Will genomic science make the final decision about whether racial realism (e.g. racial population naturalism) or anti-realism (e.g. racial scepticism) is correct? We think not. The results of even our best and most impressive genomic technologies under-determine whether biogenomic races exist, or not. First, different sub-disciplines of biology interested in population structure employ distinct concepts, aims, measures and models, producing cross-cutting categorisations of population subdivisions rather than a single, universal biogenomic concept of 'race.' Second, within each sub-discipline (e.g. phylogenetics, conservation biology), genomic results are consistent with, and map multiply to, racial realism and anti-realism. Indeed, racial ontologies are constructed conventionally, rather than discovered. We thus defend a constructivist conventionalism about biogenomic racial ontology. Choices and conventions must always be made in identifying particular kinds of groups. Political agendas, social programmes, and moral questions premised on the existence of naturalistic race should accept that no scientifically grounded racial ontology is forthcoming, and adjust presumptions, practices and projects accordingly.