Recently, domain generalization (DG) has emerged as a promising solution to mitigate distribution-shift issue in sensor-based human activity recognition (HAR) scenario. However, most existing DG-based works have merely focused on modeling statistical dependence between sensor data and activity labels, neglecting the importance of intrinsic casual mechanism. Intuitively, every sensor input can be viewed as a mixture of causal (category-aware) and non-causal factors (domain-specific), where only the former affects activity classification judgment. In this paper, by casting such DG-based HAR as a casual inference problem, we propose a causality-inspired representation learning algorithm for cross-domain activity recognition. To this end, an early-forking two-branch framework is designed, where two separate branches are respectively responsible for learning casual and non-causal features, while an independence-based Hilbert-Schmidt Information Criterion is employed to implicitly disentangling them. Additionally, an inhomogeneous domain sampling strategy is designed to enhance disentanglement, while a category-aware domain perturbation layer is performed to prevent representation collapse. Extensive experiments on several public HAR benchmarks demonstrate that our causality-inspired approach significantly outperforms eleven related state-of-the-art baselines under cross-person, cross-dataset, and cross-position settings. Detailed ablation and visualizations analyses reveal underlying casual mechanism, indicating its effectiveness, efficiency, and universality in cross-domain activity recognition scenario.