In Bohmian mechanics, the position of the particles must have a random distribution given by $\rho = |\Psi|^2$, where $\Psi$ is the wave function, in order to be compatible with Born rule in standard Quantum Mechanics. If I understand correctly, this is referred to as the quantum equilibrium hypothesis (QEH). There is a priori no reason not to consider non-quantum distributions but then an equivalent of Boltzmann H-theorem is claimed to guarantee that such a non-quantum distribution would very quickly relax to $\rho = |\Psi|^2$, and would therefore never be observed.
But then how would one evade Loschmidt's argument in this context? The equations of motions for the particles, and for the wave function, are definitively deterministic. The situation seems actually worse than in classical Newtonian mechanics since the particle do actually not have a real dynamic: the equations of motion boils down to the speed of the particle being directly determined by the wave function.