The electronic spectra of altern magnets exhibit non-trivial topology due to the interplay between time-reversal and crystalline symmetries, leading to unconventional Zeeman splitting between bands of opposite spins. This paper investigates the impact of small spin-orbit coupling (SOC) on the electronic spectrum of altern magnets, focusing on two-dimensional (2D) and three-dimensional (3D) models. The direction of magnetic moments in the altern magnetic state significantly influences the electronic spectrum, enabling novel topological phenomena. In 2D, the SOC gaps out the Dirac crossings between bands of the same spin but opposite sublattices, resulting in mirror Chern bands that support a quantum spin Hall effect. In 3D, these crossings persist even with SOC, forming Weyl nodal loops protected by mirror symmetry. The study highlights the generic existence of topological nodal crossings and the role of magnetic moment direction in determining their fate. The findings offer new avenues for realizing mirror Chern insulators and Weyl nodal loops in altern magnetic materials.The electronic spectra of altern magnets exhibit non-trivial topology due to the interplay between time-reversal and crystalline symmetries, leading to unconventional Zeeman splitting between bands of opposite spins. This paper investigates the impact of small spin-orbit coupling (SOC) on the electronic spectrum of altern magnets, focusing on two-dimensional (2D) and three-dimensional (3D) models. The direction of magnetic moments in the altern magnetic state significantly influences the electronic spectrum, enabling novel topological phenomena. In 2D, the SOC gaps out the Dirac crossings between bands of the same spin but opposite sublattices, resulting in mirror Chern bands that support a quantum spin Hall effect. In 3D, these crossings persist even with SOC, forming Weyl nodal loops protected by mirror symmetry. The study highlights the generic existence of topological nodal crossings and the role of magnetic moment direction in determining their fate. The findings offer new avenues for realizing mirror Chern insulators and Weyl nodal loops in altern magnetic materials.