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From an RP standpoint: Yes, since there is no expression for enemies to attempt to capture you in the game, killing on sight is a reasonable action. Moreover, it's clear while Malak preferred to take her alive, he wasn't that concerned about it given he ordered the entire planet destroyed just to remove her as a factor once it became obvious he wouldn't find her. An easy solution would have been to just have a quest in the game that allowed you to find a disguise for her, but I guess Bioware never thought of it. It's amusing though that for some reason they made a huge deal of her being recognized on Korriban, but not on Taris, despite all of the Sith actively looking for her there. Lol. As an aside though, it doesn't make sense for any of your Force Sensitive party members to be allowed on Korriban, since Uthar or Yuthura would pick up on their sensitivity immediately and the jig would be up.

I think this could work if done well. I've always thought it was funny that she could just run around Taris in her signature clothes, waving her lightsaber in everyone's face. And even the official cover art shows her fighting a Dark Jedi in the Upper City, as others have pointed out before. But it could definitely feel clunky and annoying if implemented poorly. I like the idea behind Operation Kill Bastila, but it seems odd just to give her a hood lol. Maybe another set of clothes/armor could be added to the inventory after the Brejik encounter? Maybe some variant of the commoner clothing?

You attack the Sith throughout the game with Bastila in your party, and none of them says "Lord Malak wants her captured alive!" Malak surely wouldn't prioritize a soldier or officer over Bastila, it's obviously game mechanics. So, the limited game mechanic means Sith should attack Bastila on sight. OTOH, the Sith officers and soldiers are often stupid...