Actually, THAT Sypha is a very young, brash, and heavily idealistic one.
As Trevor points out, this is waaaaaaay before they had even met.
Remember, the Sypha from Judgment is from the past, from before the Church sends her in her covert mission to the Wallachian countryside.
You know, that mission in which she failed and got Petrified for an undisclosed period of time.
It is possible that, while standing there in the Cyclops's collection for who-knows-how-long, she has had time to think about many things.
It is also possible that in the time between the events of Judgment and the events leading up to Castlevania III, she matured her stance on many aspects of her life.
The way Sypha speaks to Trevor, whether you choose to accept or reject her offer to help, is very polite, and even kind-hearted. Her words don't have the edge they had when she was a young annoying
Knight Templar.
In her CVIII ending, the game states that she 'has had a bad life but is beginning to feel more comfortable with herself'. It's possible that this has the added effect of taking that edge off of her old ideals and she's become less black-and-white about things, including other supernatural forces which may or may not be evil.
It's possible that, if the CVIII canon is meant to be believed, and they ALL saved the countryside together, that her brief time spent with Alucard, a creature of Darkness, helped to change her stance.