The rapid aging of societies is intensifying demand for autonomous care robots; however, most existing systems are task-specific and rely on handcrafted preprocessing, limiting their ability to generalize across diverse scenarios. A prevailing theory in cognitive neuroscience proposes that the human brain operates through hierarchical predictive processing, which underlies flexible cognition and behavior by integrating multimodal sensory signals. Inspired by this principle, we introduce a hierarchical multimodal recurrent neural network grounded in predictive processing under the free-energy principle, capable of directly integrating over 30,000-dimensional visuo-proprioceptive inputs without dimensionality reduction. The model was able to learn two representative caregiving tasks, rigid-body repositioning and flexible-towel wiping, without task-specific feature engineering. We demonstrate three key properties: (i) self-organization of hierarchical latent dynamics that regulate task transitions, capture variability in uncertainty, and infer occluded states; (ii) robustness to degraded vision through visuo-proprioceptive integration; and (iii) asymmetric interference in multitask learning, where the more variable wiping task had little influence on repositioning, whereas learning the repositioning task led to a modest reduction in wiping performance, while the model maintained overall robustness. Although the evaluation was limited to simulation, these results establish predictive processing as a universal and scalable computational principle, pointing toward robust, flexible, and autonomous caregiving robots while offering theoretical insight into the human brain's ability to achieve flexible adaptation in uncertain real-world environments.