I am curious as to how?
If, we take as axiomatic that there is no such thing as "an object in motion", only "an object in motion with respect to another object", i.e. motion is not a property of an object, but a relation between two objects.
And that since it's 4.3 light-years to Alpha Centauri, therefor a cause (e.g. a radio wave) sent from Earth today cannot have an effect (e.g. an Astronomer writes a paper about it) at Alpha Centauri for 4.3 years, and vice versa. There is 4.3 years of "Absolute elsewhere" to get through first where there is no possible cause-and-effect relation between events. At the other side of our galaxy it's around 100 000 years. And further out, objects are not just far, but receding from us (or us from them, equivalently)
Assuming an unbounded and expanding universe, for very distant parts of the universe receding from us at lightspeed (or speeds faster than light?) and us from them, equivalently. So lightspeed signals from there never reach us, by definition? That part is is utterly unobservable, permanently Absolute elsewhere. The universe's observable edge is a slowed-down red-shift that trails off into the unobservable. In other words, the at no time in the future will those signals have an effect on Earth, or us on them. So, they can't have an effect in our future, let alone our past. No impact to causality at all?