In this Letter, we theoretically investigate the application of a bistable Fabry-Perot semiconductor laser under optical injection as an all-optical activation unit for multilayer perceptron optical neural networks. The proposed device is programmed to provide reconfigurable sigmoid-like activation functions with adjustable thresholds and saturation points and benchmarked on machine learning image recognition problems. Due to the reconfigurability of the activation unit, the accuracy can be increased by up to 2% simply by adjusting the control parameter of the activation unit to suit the specific problem. For a simple two-layer perceptron neural network, we achieve inference accuracies of up to 95% and 85%, for the MNIST and Fashion-MNIST datasets, respectively.