Swarms of soft microrobots controlled by minimally invasive magnetic fields show promise as potential biomedical agents. The collective behaviour of such swarms, governed by magnetic and hydrodynamic interactions, emerges from the properties of their individual constituents. The introduction of anisotropy into microrobots, including both magnetic and structural anisotropy, expands the possibilities space for tailoring and predetermining the interactions and collective behaviours that result. However, the methods best suited for large-scale production of soft microrobots, such as emulsion-based synthesis, typically result in isotropic characteristics. In this work, by combining simulation-guided design and droplet-based microfluidics, we develop a versatile, high-throughput technique for fabricating soft microrobots with programmable structural and magnetic anisotropy. Our microrobots consist of iron oxide nanoparticles organized into supradomain structures and entrapped in a hydrogel matrix that can be elongated independently of its magnetic properties. By applying rotating magnetic fields to resulting swarms, distinct collective behaviours are produced, including gas-like, variable crystal, stable crystal, and heterogeneous motions.