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.