  We theoretically and experimentally study the stability of the unconventional
fractional antiferromagnetic skyrmion lattice (AF-SkL) in Mn$_2$S$_4$ 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 Ref. [S. Gao, et al., Nature 586, 37-41 (2020)], we
show that the skyrmion lattice is aligned within the equivalent and symmetric
$[$1-11$]$ or $[$1-11$]$ planes, which are equally inclined to the applied
magnetic field. 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 B// $[$1-10$]$. The
present study elucidates the central role of the magnetic anisotropy in the
stabilization of antiferromagnetic skyrmionic states.
