It is rarely appreciated that the Novikov self-consistency principle is a trivial consequence of the uniqueness of the metric tensor (up to diffeomorphisms) in GR.

Indeed, given that (a neighborhood of) each spacetime point, even in a spacetime with CTCs, has a unique metric, it also has unique stress-energy tensor derived from this metric (you neighborhoods to do derivatives). So there is a unique matter content at each spacetime point. In other words, your grandfather cannot be alternately alive (first time through the loop) or dead (when you kill him the second time through the loop) at a given moment in space and time.

The unfortunate fact that we can even imagine the grandfather paradox to begin with is due to our intuitive thinking that that the spacetime is only a background for "real events", a picture as incompatible with GR as perfectly rigid bodies are with SR.