The nice thing about relativity (special and general) is that all of the weird seeming-paradoxes 'sort themselves out' eventually. In particular, whilst we lose a total ordering for events, we never lose causality; i.e. two events can only appear in a different order to different observers if those two events are independent (no information has travelled between them, and hence neither one can influence the other).

It's reasonably straightforward to build systems under such constraints; e.g. see https://en.wikipedia.org/wiki/Relativistic_programming