As automated face recognition applications tend towards ubiquity, there is a growing need to secure the sensitive face data used within these systems. This paper presents a survey of biometric template protection (BTP) methods proposed for securing face "templates" (images or representative features) in neural-network-based face recognition systems. The BTP methods are categorised into two types: Non-NN and NN-learned. Non-NN methods use a neural network (NN) as a feature extractor, but the BTP part is based on a non-NN algorithm applied at either image-level or feature-level. In contrast, NN-learned methods specifically employ a NN to learn a protected template from the unprotected face image or features. We present examples of Non-NN and NN-learned face BTP methods from the literature, along with a discussion of the two categories' comparative strengths and weaknesses. We also investigate the techniques used to evaluate these BTP methods, in terms of the three most common BTP criteria: "recognition accuracy", "irreversibility", and "renewability/unlinkability". As expected, the recognition accuracy of protected face recognition systems is generally evaluated using the same (empirical) techniques employed for evaluating standard (unprotected) biometric systems. On the contrary, most irreversibility and renewability/unlinkability evaluations are found to be based on theoretical assumptions/estimates or verbal implications, with a lack of empirical validation in a practical face recognition context. We recommend, therefore, a greater focus on empirical evaluation strategies, to provide more concrete insights into the irreversibility and renewability/unlinkability of face BTP methods in practice. Additionally, an exploration of the reproducibility of the studied BTP works, in terms of the public availability of their implementation code and evaluation datasets/procedures, suggests that it would currently be difficult for the BTP community to faithfully replicate (and thus validate) most of the reported findings. So, we advocate for a push towards reproducibility, in the hope of furthering our understanding of the face BTP research field.