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Superconducting Bogoliubov Fermi surfaces require broken time-reversal symmetry to be realized. Recently, this has been examined  in multiorbital superconductors that preserve inversion symmetry [1]. In this case, the resultant Bogoliubov Fermi surfaces are topologically protected. However, despite the lack of topological protection, they can also appear when both time-reversal and inversion symmetries are broken. Here we examine the development of Bogoliubov Fermi surfaces due to magnetic toroidal order, magnetic order that breaks both time-reversal and inversion symmetries but preserve their product [2,3]. We show that the nematic Bogoliubov Fermi surfaces observed in tetragonal FeSe_1-xS_x [4] are naturally explained if such a toroidal magnetic order coexists with superconductivity [3]. We further show that Néel (checkerboard) magnetic order or pair density wave superconductivity both give rise to magnetic toroidal order consistent with the observed nematic Bogoliubov Fermi surfaces.