Causality means that any transmission of information from event A to event B means that event A must precede B in time. An example would be an electron emitter emitting an electron, and a detector detecting an electron. If the detector went off before the electron was emitted, that would be a violation of causality.
Relativity of simultaneity does nothing to prevent such a global evaluation, it only restricts the sets of events that could possibly be causes of other events.
As long as events A and B are separated by a time-like distance, then while individual observers may disagree on the exact timing of A and B, all will agree on their ordering. It's only when A and B are separated by space-like distances that different observers will disagree on their ordering. And therefore, if it was possible to send information that could get outside of your future light-cone, then that information could be relayed around between several reference frames and back to you, arriving before you sent it in the first place according to all observers, creating a paradox.
This is the foundation of the argument against FTL information transfer, the Paradox in the EPR Paradox. It's why it's important for maintaining QM's consistency with Special Relativity that quantum entanglement is not capable of sending information.
The circumstances that allow time paradoxes in Special Relativity while allowing FTL communication are somewhat exotic. If we just allow retrograde causality in any given experiment then it should become trivial to create a paradox. Alice conducts and experiment that transmits information Bob. After receiving the result, Bob conducts his experiment which sends information in the opposite time direction back to Alice prior to her conducting her experiment. As per their previously agreed upon protocol, if Alice receives information from Bob she does not conduct her experiment. Paradox.
There's no requirement that one direction in time be singled out as special, but whichever way you go everything else should be going in the same direction. If you time reverse the evolution of the solar system everything works, but not if you only reverse time for the Moon while the rest of the solar system evolves in the usual direction. Can anything but our experience/the 2nd law say that one is the "future" and one the "past". No, but if you picked one by arbitrary convention, then everyone else would have to agree.
If there's a form of retrocausality that allows it to occur with respect to other forward-causality events without allowing for paradoxes, that'd be quite interesting.