Iris recognition is widely used in high-security scenarios due to its stability and distinctiveness. However, the acquisition of iris images typically requires near-infrared illumination and near-infrared band filters, leading to significant and consistent differences in imaging across devices. This underscores the importance of developing cross-domain capabilities in iris anti-spoofing methods. Despite this need, there is no dataset available that comprehensively evaluates the generalization ability of the iris anti-spoofing task. To address this gap, we propose the IrisGeneral dataset, which includes 10 subsets, belonging to 7 databases, published by 4 institutions, collected with 6 types of devices. IrisGeneral is designed with three protocols, aimed at evaluating average performance, cross-racial generalization, and cross-device generalization of iris anti-spoofing models. To tackle the challenge of integrating multiple sub-datasets in IrisGeneral, we employ multiple parameter sets to learn from the various subsets. Specifically, we utilize the Mixture of Experts (MoE) to fit complex data distributions using multiple sub-neural networks. To further enhance the generalization capabilities, we introduce a novel method Masked-MoE (MMoE). It randomly masks a portion of tokens for some experts and requires their outputs to be similar to the unmasked experts, which improves the generalization ability and effectively mitigates the overfitting issue produced by MoE. We selected ResNet50, VIT-B/16, CLIP, and FLIP as representative models and benchmarked them on the IrisGeneral dataset. Experimental results demonstrate that our proposed MMoE with CLIP achieves the best performance on IrisGeneral.