The pronouns they/them/their are readily available with a singular interpretation as bound variables (Balhorn 2004, Bjorkman 2017). Referential interpretations are possible, but subject to pragmatic considerations and changes in progress (Bjorkman 2017, Conrod 2019, Konnelly and Cowper 2020). In a series of experiments, we tested differences between bound and referential singular they in acceptability and incremental processing, asking whether bound they is sensitive to the gender of its antecedent, as referential they is (Doherty and Conklin 2017, Ackerman 2018, Ackerman et al. 2018, Conrod 2019). We found that bound singular they has an advantage over referential singular they in acceptability, even when the antecedent is gendered. In processing, however, bound-variable singular they showed a reading time advantage over referential singular they only with gendered antecedents. We evaluate these results against existing formal linguistic theories of singular they implemented within psycholinguistic models of pronoun processing. We submit that none of the theories fully captures the range of evidence we uncover, in particular the interaction between gender and quantification. We suggest a formal account that does: we propose, using representations from Kratzer (2009) and Sudo (2012), that gender and number features are differentially represented in referential versus binding dependencies. We speculate how this representational difference relates to the processing mechanisms of antecedent retrieval and to the limited processing advantage for bound singular they that we found.