Optical surveys have become increasingly adept at identifying candidate tidal disruption events (TDEs) in large numbers, but classifying these generally requires extensive spectroscopic resources. Here we present tdescore, a simple binary photometric classifier that is trained using a systematic census of ∼3000 nuclear transients from the Zwicky Transient Facility (ZTF). The sample is highly imbalanced, with TDEs representing ∼2% of the total. tdescore is nonetheless able to reject non-TDEs with 99.6% accuracy, yielding a sample of probable TDEs with recall of 77.5% for a precision of 80.2%. tdescore is thus substantially better than any available TDE photometric classifier scheme in the literature, with performance not far from spectroscopy as a method for classifying ZTF nuclear transients, despite relying solely on ZTF data and multiwavelength catalog cross matching. In a novel extension, we use "Shapley additive explanations" to provide a human-readable justification for each individual tdescore classification, enabling users to understand and form opinions about the underlying classifier reasoning. tdescore can serve as a model for photometric identification of TDEs with time-domain surveys, such as the upcoming Rubin observatory.