Why is Shadow being referred to as a woman?

Solution 1:

According to this GameFaqs post, this was due to a programming error in the original SNES version.

As a result of events prior in the story, the individual you find wounded in the cave is either Shadow (male) or Relm (female). The error incorrectly displays the text as "her" even if Shadow is the one that is found. This was corrected in the PSX release.

First off, the SNES and PSX versions are almost exactly the same, except that in the PSX version, the Sketch bug was fixed (as opposed to only some SNES versions), there were a few MINOR dialog changes (most notable that the "Let's take her back to Thamasa" line was corrected, so it matches the proper gender of the charcter being referred to (female if Relm, male if Shadow)).

_{(Emphasis my own)}

This is confirmed on the IGN's game script

Hey, wasn't that... Interceptor!?

Look at those wounds...

Enemy's coming from behind! Another monster appeared!

We can't do anything for him here. Let's take him back to Thamasa using the airship.

_{(Emphasis my own)}

As for the GBA release, the dialog in this scene seems to have been changed entirely and, in turn, removed the gender specific text, as shown in the GameFaq's game script

[The party enters into the cave and Interceptor comes toward them.]

Are you trying to tell me to follow you?

These wounds are awful...

[The party enters into a battle with a monster.]

Something's coming from behind!

We can't do anything for wounds like these here... Let's fly back to Thamasa on the double.

_{(Emphasis my own)}