We report muon spin rotation experiments on the magnetic penetration depth λ and the temperature dependence of λ^-2 in the over-doped Fe-based high-temperature superconductor (Fe-HTS) Ba_1-xRb_xFe₂As₂ (x = 0.65) studied at ambient and under hydrostatic pressures up to p = 2.3 GPa. We find that in this system λ^-2(T) is best described by d-wave scenario. This is in contrast to the case of the optimally doped x = 0.35 system which is known to be a nodeless s^+--wave superconductor. This suggests that the doping induces the change of the pairing symmetry from s^+- to d wave in Ba_1-xRb_xFe₂As₂. In addition, we find that the d-wave order parameter is robust against pressure, suggesting that d is the common and dominant pairing symmetry in over-doped Ba_1-xRb_xFe₂As₂. Application of pressure of p = 2.3 GPa causes a decrease of λ(0) by less than 5%, while at optimal doping x = 0.35 a significant decrease of λ(0) was reported. The superconducting transition temperature T_c as well as the gap to T_c ratio 2Δ/k_BT_c show only a modest decrease with pressure. By combining the present data with those previously obtained for optimally doped system x = 0.35 and for the end member x = 1, we conclude that the SC gap symmetry as well as the pressure effects on the SC quantities strongly depend on the Rb doping level. These results are discussed in the light of the putative Lifshitz transition, i.e., a disappearance of the electron pockets in the Fermi surface of Ba_1-xRb_xFe₂As₂ upon hole doping.