  We present an in-depth classification of the topological phases and Majorana
fermion (MF) excitations that arise from the bulk interplay between
unconventional multiband spin-singlet superconductivity and various magnetic
textures. We focus on magnetic texture crystals with a periodically-repeating
primitive cell of the helix, whirl, and skyrmion types. Our analysis is
relevant for a wide range of layered materials and hybrid devices, and accounts
for both strong and weak, as well as crystalline topological phases. We
identify a multitude of accessible topological phases which harbor flat, uni-
or bi-directional, (quasi-)helical, or chiral MF edge modes. This rich variety
of MFs originates from the interplay between topological phases with gapped and
nodal bulk energy spectra, with the resulting types of spectra and MFs
controlled by the size of the pairing and magnetic gaps.
