We present a new framework for generic mixed-protocol secure two-party computation (2PC) and private evaluation of neural networks based on the recent MOTION framework (Braun et al., ePrint '20). We implement five different 2PC protocols in the semi-honest setting -- Yao's garbled circuits, arithmetic and Boolean variants of Goldreich-Micali-Wigderson (GMW), and two secret-sharing-based protocols from ABY2.0 (Patra et al., USENIX Security '21) -- together with 20 conversions among each other and new optimizations. We explore the feasibility of evaluating neural networks with 2PC without making modifications to their structure, and provide secure tensor data types and specialized building blocks for common tensor operations. By supporting the Open Neural Network Exchange (ONNX) file format, this yields an easy-to-use solution for privately evaluating neural networks, and is interoperable with industry-standard deep learning frameworks such as TensorFlow and PyTorch. By exploiting the networks' high-level structure and using common 2PC techniques, we obtain a performance that is comparable to that of recent, highly optimized works and significantly better than when using generic 2PC for low-level hybrid circuits.