Environment is assumed to play a negative role in quantum mechanics, destroying the coherence in a quantum system and, thus, randomly changing its state. However, for a quantum system that is initially in a degenerate ground state, the situation could be different. In this case, the infinite manifold of ground state eigenfunctions can contain a few states of zero entanglement, which can be demonstrated based on the minimization of the von Neumann entropy. Then, following quantum Darwinism, these "classical" combinations are selected and promoted by the quantum environment, which means that different independent observers find them in experiments. In this work, we find and explore such classical states in the eigenspectra of skyrmionic and antiferromagnetic quantum systems starting from a numerical realization of Anderson's tower of states. The degeneracy of the quantum ground state is shown to be the key for explaining nontrivial properties of magnetic matter in the classical world including topological protection arising in the classical limit.