Typical nonthermal features of ion velocity distributions observed in the fast solar wind are the relative streaming between two proton components, an alpha/proton relative flow, and anisotropic proton cores with T⊥p > T∥p, where the subscripts denote directions relative to the background magnetic field B0. All these nonthermal features lead to the growth of the several electromagnetic instabilities. Here, linear Vlasov theory and one-dimensional hybrid simulations are used to study these instabilities in a homogeneous, magnetized, and collisionless plasma model. Under these conditions, both magnetosonic and Alfv¿n/cyclotron modes become unstable. We show that for conditions typical of the fast solar wind and parallel propagation, the proton core temperature anisotropy plays a significant role in modifying the wave-particle scattering of each ion component as compared to the isotropic case. Such an effect leads to a reduction in both the heating and anisotropy enhancement of the proton beam and alpha component and to a decrease in the relative proton/proton and proton/alpha flow speeds below the corresponding isotropic instability thresholds. This result provides additional support to the physical scenario in which instability thresholds correspond to observable constraints on plasma species anisotropies and match closer recent solar wind observations.