In Special Relativity, relative speeds greater than light inevitably lead to frames of reference where travel into the past happens. Because of the problems with causality this creates, it is then assumed that faster than light travel through local space is impossible.
But now many theorists are convinced that General Relativity has consistant solutions (wormholes) that allow travel into the past to occur. If time travel is possible, then why is the “ban” on FTL travel through local space retained?
You’re confusing two Special Relativity consequences which are separate. One is that as matter is accelerated, it gains mass. By the time it reaches c (speed of light in vacuum) it would have gained infinite mass, and to do that requires an infinite amount of energy. So it is impossible to accelerate normal matter to c. This is in good agreement with observations.
A separate consequence is that if you can somehow move faster than c, you will be able to transmit information to the past. (I can’t remember if you can also move normal matter to the past - I think it’s possible.) Therefore, it means that faster-than-light travel breaks causality. Many people take that as a proof that FTL travel is impossible, but some think that causality can be broken - we just don’ t know what happens when it is broken. People who propose tachyons (faster-than-light particles) and wormholes are in the latter group.
Tachyons can be described in an inertial reference frame, so you can speak of tachyons in Special Relativity and ask whether they could exist. (I think not because of the causality problems.)
Wormholes cannot be described in an inertial reference frame and so require the General Theory of Relativity. You only have a causality problem if information can be transmitted back in time.
Basically, with a wormhole, you’ve got an extra path from point A to point B, shorter than the “normal” path. That alone is enough to make the wormhole FTL. Anything other than that (forces inside, etc) is currently mostly in the realm of speculation.