Waves and instabilities have very often been an object of fascination since the introduction of non-Maxwellian features in space plasmas. To date, the dispersion relation, including real frequency, damping, and growth rates of magnetosonic waves has been studied in many different types of non-Maxwellian distributions. However, these characteristics have been overlooked in the temperature bi-anisotropic Cairns distribution, characterized by the free parameter Λ. By employing the linearized Vlasov–Maxwell system in homogeneous plasma, the dispersion relation is analytically solved. It is found that the non-Maxwellian features, Λ ≠ 0 along with electron temperature anisotropy, notably modify the real frequency, damping, and growth rates—both in the hydrodynamic as well as in the kinetic regimes. Interestingly, the growth rate in the kinetic regime is entirely due to the correlation of Λ with the electron temperature anisotropy which is otherwise absent in the Maxwellian distribution. Due to their relevance, the results are applicable to solar wind plasma.