We theoretically and experimentally study the stability of the unconventional fractional antiferromagnetic skyrmion lattice (AF-SkL) in MnSc2S4 spinel under magnetic fields applied along the [1-10] crystal direction. By performing numerical Monte Carlo simulations for the minimal effective spin model that we proposed in S. Gao, Nature 586, 37 (2020)0028-083610.1038/s41586-020-2716-8, we show that the lattice is aligned within the equivalent and symmetric [1-11] or [1-1-1] planes, which are equally inclined to the applied magnetic-field H. We attribute this behavior to the magnetic anisotropy of the host material. Neutron single-crystal diffraction presents a very good agreement with the predictions of the effective model. It reveals that the topological spin texture gets destabilized at low temperatures and moderate magnetic fields and is replaced by a conical phase for H// [1-10]. The present study elucidates the central role of the magnetic anisotropy in the stabilization of AF-Sk states.