I'm trying to figure out why Azula has a Scarlet Contract? That, and given her being a half-breed, how is Celestia walking around town with her head still attached to her neck?
Since the scarlet law wasn't created by humans, I think it applies to EVERY female who's unmarried.
I'm pretty sure this also includes the princess, the half breeds and all vala.
Half breeds are distrusted to a massive degree, but are also known to be pets sometimes.
As the person up a bit said, the law protects your property from assault, as well as you being responsible for their behaviour.
So it's just: Are you willing to take the risk?
We, as the MC, are willing cause we like her.
At the beginning of the game, it states pretty empathically that half-breeds are to be killed on sight. Celestia's having possibly been someone's pet at one time indicates that she is likely a runaway, and being sought by her owner. She should be hiding, not blackmailing the MC. I would have told her 'Hey great, let's go see the Holy Knights together." and sat back to watch what happened next.
That's because most of them are violent and a menace.... but there are some who arn't and our little fluffball is one of those who's merely a bit annoying. :-p
As to her being a pet previously, the princess already knows this, but she also knows that the person she was the pet to is the person who had the future prediction thingamjig.
So she knows If they did what you suggest, they'd never have any chance to find the predictive thing which the princess is looking for.
Also the mc has been kissing the princess butt since the start, so she trusts him to possibly find the thing by befriending the fluffbal.