I really like the headcanon explanations for this variation of Revan's story that this mod allows for. Here's a couple of examples I thought of:
1. The reason Carth and the player rescued Bastila on Taris was to get her back to the Fleet so she could use her Battle Meditation to win victories and save lives. But this is completely forgotten on Dantooine! A player who is a Republic Soldier or Scout should strongly object to Bastila wasting time training a Jedi apprentice on Dantooine (a peacetime Jedi activity) rather than returning to the Fleet and helping win the war. Master Vandar never discussed Bastila's future agenda with Admiral Dodonna - I bet the Admiral would have been absolutely horrified and very angry! How many Republic ships and crews would be lost in battle with the Sith because Bastila was on Dantooine for months? No other Jedi in this time had her ability.
2. A player who is a Scoundrel would likely take a VERY dim view of committing the rest of their entire life to the Jedi Order, and giving up their freedom permanently. Even a Republic Soldier or Scout has only signed up for the duration of the war. Scoundrels would really value their freedom and independence very highly, and should only agree to help the Republic in wartime, to save their home. Many would only agree to Republic army service as an alternative to being stuck in prison!
3. A player who naturally leans toward the Dark Side would not want the Jedi Order to pry too closely into their feelings and motivations, and the bond with Bastila makes concealment of dark emotions very difficult, if not completely impossible. Refusing the Jedi training misses out on the massive power gain of learning the ways of the Force, but at least it allows the player a better chance of staying away from Bastila and hopefully escaping from the Jedi Order at the earliest opportunity.