glTF 2.0 skinned animations work! You can export such animations from Blender and a lot of other software.
Sample models:
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Khronos glTF sample models include some skin animations, like CesiumMan, Fox, BrainStem.
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Sample skinned animation created in latest Blender (2.82a). Exported to glTF using standard Blender -> X3D exporter, without any tweaks or custom exporters necessary. Just export and it works 🙂