Gender-neutral pronouns are increasingly being introduced across Western languages. Recent evaluations have however demonstrated that English NLP systems are unable to correctly process gender-neutral pronouns, with the risk of erasing and misgendering non-binary individuals. This paper examines a Dutch coreference resolution system's performance on gender-neutral pronouns, specifically hen and die. In Dutch, these pronouns were only introduced in 2016, compared to the longstanding existence of singular they in English. We additionally compare two debiasing techniques for coreference resolution systems in non-binary contexts: Counterfactual Data Augmentation (CDA) and delexicalisation. Moreover, because pronoun performance can be hard to interpret from a general evaluation metric like LEA, we introduce an innovative evaluation metric, the pronoun score, which directly represents the portion of correctly processed pronouns. Our results reveal diminished performance on gender-neutral pronouns compared to ... : 22 pages, 2 figures. Accepted at the 2024 ACM Conference on Fairness, Accountability, and Transparency (FAccT '24) ...