All Special Relativity requires is that space be more or less flat between point A and point B. It doesn't matter if the information travels from A to B through a wormhole and then into another universe and then out the butt of Dumbo, if it ends up at B before light would, then causality has been violated.
If, on the other hand, your FTL drive bends up space all around us to be like a giant hyperspace pretzel, (1) we're going to have a lot more problems than just a little violation of causality, and (2) causality still ends up being violated via General Relativity.
Causality is a consequence of the physical laws you are currently using, not a law in themselves. It just paints a logical boundary condition around what is possible using the current set of laws that you are using.
Compare Newtonian causality where there is only one timeframe everywhere to SR causality with its local timeframes to GR which supports warping of space and time. All different and not interchangable.
Wormholes cannot exist in SR, therefore applying SR's brand of causality is equally invalid. Under GR the concept of simultaneity is relaxed: the effect is only limited to the light cone of the cause.
Special Relativity is not invalidated by GR: Special Relativity is a special case of GR that tells us what to expect in inertial frames in a flat space. As long as points A and B are in a flat enough space, then the predictions of Special Relativity about the causal nature of information transmitted between A and B BY ANY MEANS will still be true, even if there are nearby wormholes. If Special Relativity tells us that we can make a closed causal loop via the FTL signals that make it through a wormhole, then GR will not overturn this, no matter how the information made it from A to B.
I agree that if the space Between A and B is distorted enough so that the light that travels in open space between A and B is seriously affected by a curvature that extends from A to B, then it is true that you cannot use SR to make your predictions, as the premises of SR are violated. But then GR will predict that causality can be violated anyway. (It's generally easier to find ways to violate causality in GR that SR anyway, since it doesn't require FTL transmissions of information in GR to create causal loops.)
I refer you to the FTL faq, since it seems that I am not able to talk sense into people on my own:
If, on the other hand, your FTL drive bends up space all around us to be like a giant hyperspace pretzel, (1) we're going to have a lot more problems than just a little violation of causality, and (2) causality still ends up being violated via General Relativity.