Extended reality (XR) systems, which consist of virtual reality (VR), augmented reality (AR), and mixed reality (XR), offer a transformative interface for immersive, multi-modal, and embodied human-computer interaction. In this paper, we envision that multi-modal multi-task (M3T) federated foundation models (FedFMs) can offer transformative capabilities for XR systems through integrating the representational strength of M3T foundation models (FMs) with the privacy-preserving model training principles of federated learning (FL). We present a modular architecture for FedFMs, which entails different coordination paradigms for model training and aggregations. Central to our vision is the codification of XR challenges that affect the implementation of FedFMs under the SHIFT dimensions: (1) Sensor and modality diversity, (2) Hardware heterogeneity and system-level constraints, (3) Interactivity and embodied personalization, (4) Functional/task variability, and (5) Temporality and environmental variability. We illustrate the manifestation of these dimensions across a set of emerging and anticipated applications of XR systems. Finally, we propose evaluation metrics, dataset requirements, and design tradeoffs necessary for the development of resource-aware FedFMs in XR. This perspective aims to chart the technical and conceptual foundations for context-aware privacy-preserving intelligence in the next generation of XR systems.