In this paper, we study space fractional Cahn-Hilliard equations. A second-order stabilized finite difference scheme is exploited for the model equations. The resulting coefficient matrix is a nonsymmetric ill-conditioned Toeplitz-like matrix. Symmetrized strategies are proposed for the nonsymmetric system so that the conjugate gradient method can be utilized to derive the numerical solutions. Moreover, preconditioners based on the sine transform are designed to speed up the convergence rate of the proposed methods. Theoretically, we prove that the spectra of the preconditioned matrices are uniformly bounded in the interval (1/2, 3/2), which guarantees that the preconditioned conjugate gradient method converges linearly, within an iteration number independent of the matrix size. Numerical experiments are reported to show the effectiveness of the proposed methods.