Recently, federated multi-view clustering (FedMVC) has emerged to explore cluster structures in multi-view data distributed on multiple clients. Existing approaches often assume that clients are isomorphic and all of them belong to either single-view clients or multi-view clients. Despite their success, these methods also present limitations when dealing with practical FedMVC scenarios involving heterogeneous hybrid views, where a mixture of both single-view and multi-view clients exhibit varying degrees of heterogeneity. In this paper, we propose a novel FedMVC framework, which concurrently addresses two challenges associated with heterogeneous hybrid views, i.e., client gap and view gap. To address the client gap, we design a local-synergistic contrastive learning approach that helps single-view clients and multi-view clients achieve consistency for mitigating heterogeneity among all clients. To address the view gap, we develop a global-specific weighting aggregation method, which encourages global models to learn complementary features from hybrid views. The interplay between local-synergistic contrastive learning and global-specific weighting aggregation mutually enhances the exploration of the data cluster structures distributed on multiple clients. Theoretical analysis and extensive experiments demonstrate that our method can handle the heterogeneous hybrid views in FedMVC and outperforms state-of-the-art methods. The code is available at \url{https://github.com/5Martina5/FMCSC}.