The results of theoretical and experimental study of propagation and transformation of circularly symmetrical fields of TE vortices and linearly polarized azimuthally symmetric fields of TE and TM modes in a locally isotropic inhomogeneous medium of low-mode optical fibers are presented. The propagation constant for CV vortices as well as for TE and TM modes, as a scalar approximation of the wave equation, is shown to be fourfold degenerated with respect to topological charge and spirality. As a result of spin-orbital interaction in the eigenmodes field, the line of the propagation constant splits into four lines. The distance between the lines is equal to polarization corrections db to fields of eigenmodes. The form of the spin-orbit interaction operator is presented. The action of the operator onto fields of CV vortices, TE- and TM-modes is shown to induce topological birefringence in the locally isotropic medium of optical fibers. The birefringence manifests itself experimentally in the joint Rytov–Magnus effect.