I guess maybe we could someday find an exception to causality, but it would be a way bigger deal than any other discovery we've made. It would be a back to square one situation.
As they say, you can have FTL, relativity, or causality--pick two. We've really nailed down relativity and causality. It's not looking great for FTL. Trust me, it breaks my heart every time I think about it. But that's the way it is sometimes.
Half of QM (or its interpretations) is also "logically inconsistent", though.
>Causes happen before effects, not ever the other way around.
That's from our own perspective though. In certain theories of the universe (even ones consistent with relativity: https://en.wikipedia.org/wiki/G%C3%B6del_metric) time is not the one way stream we conceive it to be.
Godel's metric have nothing to do with reality if you actually read about it's properties. For example, the universe described by it would have no reshift for distant objects.
Please, check your facts. Otherwise you sound just like an uneducated new-ager looking for "truth".