An elementary prediction of the quantization of the gravitational field is that the Newtonian interaction can entangle pairs of massive objects. Conversely, in models of gravity in which the field is not quantized, the gravitational interaction necessarily comes with some level of noise, i.e., non-reversibility. In this talk, I will give a systematic classification of a large class of possible such models consistent with the basic requirements that the non-relativistic limit is Galilean invariant and reproduces the Newtonian interaction on average. I will show that for any such model to be non-entangling, a minimal amount of noise must be injected into any experimental system. Thus, measuring gravitating systems at noise levels below this threshold would be equivalent to demonstrating that Newtonian gravity is entangling. I will analyze these general predictions in a number of experimental setups, and test it on the classical-quantum gravity models of Oppenheim et al., the Tilloy-Diosi model, as well as on a recent model of Newtonian gravity as an entropic force.