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The utilization of mechanical-bearing-based precision motion stages (MBMS) is prevalent in the advanced manufacturing industries. However, the productivity of the MBMS is plagued by friction-induced vibrations, which can be controlled to a certain extent using a friction isolator. Earlier works investigating the dynamics of MBMS with a friction isolator considered a linear friction isolator, and the source of nonlinearity in the system was realized through the friction model only. In this work, we present the nonlinear analysis of the MBMS with a nonlinear friction isolator for the first time. We consider a two-degree-of-freedom spring-mass-damper system to model the servo-controlled motion stage with a nonlinear friction isolator. The characteristic of the dynamical friction in the system is captured using the LuGre friction model. The system’s stability and nonlinear analysis are carried out using analytical methods. More specifically, the method of multiple scales is used to determine the nature of Hopf bifurcation on the stability lobe. The analytical results indicate the existence of subcritical and supercritical Hopf bifurcations in the system, which are later validated through numerical bifurcation. This observation implies that the nonlinearity in the system can be stabilizing or destabilizing in nature, depending on the choice of operating parameters.