Moiré superlattices of twisted bilayer 2D materials creating nontrivial physical effects have recently revolutionized diverse subjects across materials, optoelectronics, nanophotonics, and beyond. Here, we present moiré superlattices in higher-dimensional freespace optics, where the basic twisted lattice is not a layer of 2D material, but a propagating structured light field with periodic topological textures. The moiré structured light with flexibly tuned twist angle can generate and transit among a rich set of topologies, including skyrmionium bags, skyrmion bag superlattices, skyrmion clusters, and quasicrystals, with controlled symmetry, most of which were not discovered in any other systems. Importantly, our freespace moiré textures maintain their topologies over long-distance propagation with nondiffractive behavior and topological robustness against perturbations and obstacles. Our work unlocks higher dimensions of moiré photonics to manipulate super-resilient topologies and address the challenges of robust information transfer and encryption.