Motivated by emergent phenomena at oxide surfaces and interfaces involving transition metal oxides, we examine the ferromagnetic Kondo lattice model (FKLM) in the presence of a Rashba spin-orbit coupling (RSOC) at zero temperature using numerical techniques. We find that the main effect of the RSOC is the destruction of the ferromagnetic state present in the FKLM at low electron fillings, with the consequent suppression of conductivity. In addition, near half-filling the RSOC leads to a departure of the antiferromagnetic state of the FKLM with a consequent reduction to the intrinsic tendency to electronic phase separation. A similar behavior is observed at very low electron density in the presence of an antiferromagnetic coupling between localized spins.