Since rBb100bdca25b1 the parent inverse was always reset in
ED_object_parent (also for just changing the parent type).
This does make sense (since there is no point keeping it when e.g
changing from "Bone" to "Object" or "Vertex" to "Object", for this to
really make sense it would have to be properly recalculated anyways
which does not happen afaict).
The reported issue was that setting the prop to the same value as it was
before (e.g. from "Object" to "Object") would still reset the parent
inverse which was really unexpected since from a user standpoint,
nothing has changed here.
So in case the value does not really change, we now just early out and
skip ED_object_parent.