In recent years, cavity optomagnonics has received considerable research interest, and the notions drawn from non-Hermitian physics have also attracted attention. Based on Faraday effect and Cotton-Mouton effect, we theoretically propose a scheme to realize exceptional point (EP) in a cavity optomagnonic system. The scheme relies on Brillouin scattering (BLS), i.e., a triple-frequency resonance between the excited photon and magnon inside cavity. By exploring the dependence of the exceptional points on the system parameters, we show that the proposed EP is magnetically tunable. Regarding the applications of the magnon-induced EP, we further discuss the greatly enhanced sensitivity, which responds to two kinds of perturbation near or on the exceptional point. Moreover, we show that the tunable EP can guard against the cavity defect to maintain the optimal precision. Characterized by the mentioned features, our proposal offers a further understanding of non-Hermitian cavity optomagnonics, and it has potential in the applications for high-sensitivity quantum sensing.