The "other gender mod" simply alters the scripts.
By default, the scripts check the player's gender and return a value depending on which script is used.
The problem with that mod is that it works for some things, but not for others because some things in the game check "is the PC male" and others check "is the PC female" - there seems to be no actual standard for it.
The mod that's floating around out there simply makes the game always say "yes" - which seems to work for at least some of the romance stuff (haven't tested it all myself yet), but I know it also makes some other aspects of the game a bit odd (various NPCs will consider you the wrong gender etc).
TK's editor goes about things a little differently. It actually sets your gender to both - which believe it or not was a viable, included possible gender in the game files by default. There just wasn't a way to use or select it before.
As for why it might be breaking things.. I haven't actually looked into it, because as stated, a lot of that is in pre-compiled scripts anyway... but - I'm guessing there's a gender check for the PC before the conversation with Carth on Taris.
I've always played the game with female characters, but I get the impression he'd probably have a different demeanor towards me than the one he always has once I wake up. Perhaps having gender at both is giving some sort of error that the game doesn't know quite how to manage at that point.
Likewise, seems to me there's a dialogue option in that sequence where he asks about what you used to do. The game probably only has options at that point available for Scout, Scoundrel, and Soldier. Setting your first class to one of the 3 Jedi classes means you can't pick any of those anymore.. which again, is simply a condition the game has no idea how to check for.
Perhaps this is something that could be solved by finding and adding to the .tlk file (or is it a .dlg) for that module? I'd look into it myself, but I haven't even begun to dig into those dialogues yet and I know others have had a lot more experience and success with editing them already. (T7 or gameunlimited perhaps?)