In the novel stoichiometric iron-based material RbEuFe4As4, superconductivity coexists with a peculiar long-range magnetic order of Eu 4f states. Using angle-resolved photoemission spectroscopy, we reveal a complex three-dimensional electronic structure and compare it with density functional theory calculations. Multiple super-conducting gaps were measured on various sheets of the Fermi surface. High-resolution resonant photoemission spectroscopy reveals magnetic order of the Eu 4f states deep into the superconducting phase. Both the absolute values and the anisotropy of the superconducting gaps are remarkably similar to the sibling compound without Eu, indicating that Eu magnetism does not affect the pairing of electrons. A complete decoupling between Fe-and Eu-derived states was established from their evolution with temperature, thus unambiguously demonstrating that superconducting and a long-range magnetic orders exist independently from each other. The established electronic structure of RbEuFe4As4 opens opportunities for the future studies of the highly unorthodox electron pairing and phase competition in this family of iron-based superconductors with doping.