Optical surveys have become increasingly adept at identifying candidate Tidal Disruption Events (TDEs) in large numbers, but classifying these generally requires extensive spectroscopic resources. We here present $texttt{tdescore}$, a simple photometric classifier that is trained using a systematic census of $sim$3000 nuclear transients from the Zwicky Transient Facility (ZTF). The sample is highly imbalanced, with TDEs representing $<$2% of the total. $texttt{tdescore}$ is nonetheless able to reject non-TDEs with 99.6% accuracy, yielding a sample of probable TDEs with completeness of 77.0% and a purity of 80.3%. $texttt{tdescore}$ is thus substantially better than any available TDE photometric classifier scheme in the literature, and performs comparably well to the single-epoch spectroscopy as a method for classifying ZTF nuclear transients, despite relying solely on ZTF data and multi-wavelength catalogue crossmatching. In a novel extension, we use ‘SHapley Additive exPlanations’ (SHAP) to provide a human-readable justification for each individual $texttt{tdescore}$ classification, enabling users to understand and form opinions about the underlying classifier reasoning. $texttt{tdescore}$ serves as a model for photometric identification of TDEs with time-domain surveys, such as the upcoming Rubin observatory.