Livestock methane emissions represent 32% of human-caused methane production, making automated monitoring critical for climate mitigation strategies. We introduce GasTwinFormer, a hybrid vision transformer for real-time methane emission segmentation and dietary classification in optical gas imaging through a novel Mix Twin encoder alternating between spatially-reduced global attention and locally-grouped attention mechanisms. Our architecture incorporates a lightweight LR-ASPP decoder for multi-scale feature aggregation and enables simultaneous methane segmentation and dietary classification in a unified framework. We contribute the first comprehensive beef cattle methane emission dataset using OGI, containing 11,694 annotated frames across three dietary treatments. GasTwinFormer achieves 74.47% mIoU and 83.63% mF1 for segmentation while maintaining exceptional efficiency with only 3.348M parameters, 3.428G FLOPs, and 114.9 FPS inference speed. Additionally, our method achieves perfect dietary classification accuracy (100%), demonstrating the effectiveness of leveraging diet-emission correlations. Extensive ablation studies validate each architectural component, establishing GasTwinFormer as a practical solution for real-time livestock emission monitoring. Please see our project page at gastwinformer.github.io.