The intersection of topology, symmetry, and magnetism yields a rich structure of possible phases. In this work, we study theoretically the consequences of magnetism on IrF4, which was recently identified as a possible candidate topological nodal chain semimetal in the absence of magnetic order. We show that the spin-orbital nature of the Ir moments gives rise to strongly anisotropic magnetic couplings resembling a tetrahedral compass model on a diamond lattice. The predicted magnetic ground state preserves key symmetries protecting the nodal lines, such that they persist into the ordered phase at the mean-field level. The consequences for other symmetry reductions are also discussed.