As neural networks continue to scale, low-precision quantization is widely adopted in edge accelerators, but conventional multi-threshold activation hardware requires 2^n-1 thresholds for n-bit integer outputs, leading to rapidly increasing hardware costs. We propose GRAU, a Generic Runtime-Reconfigurable Activation-Requantization Unit that fuses batch normalization, nonlinear activation, and requantization through piecewise-linear fitting with Power-of-Two slopes. GRAU requires only basic comparators and 1-bit right shifters, while supporting mixed-precision quantization and runtime switching among post-accumulation functions, including modern nonlinear activations such as SiLU and GELU. Compared with multi-threshold activation-requantization units, GRAU reduces LUT consumption by approximately 90% or more while improving hardware efficiency, flexibility, and scalability. We further explore the trade-off between accuracy and hardware cost across different approximation settings and provide an open-source toolchain for GRAU-aware network training.