Now, I'm faced with a dilemma - do we abandon the little girl we've been sponsoring because the organization doesn't believe as we do? Even the org that Tim linked to doesn't do what Compassion does; If I could simply swap out the agencies I would!
Will the particular girl you "sponsor" actually be left without if you stop giving? Or does Compassion mostly merge funds to help an entire community of children (which is way more efficient) and then assign individual kids to sponsors merely as a way of keeping things personal with their donors?
I don't know the answer to that question. A total cynic would say the you-sponsor-this-child thing is only a marketing trick to keep you giving forever. But I suspect Compassion has more integrity than that, and there are at least some ways in which your giving directly helps that particular girl. How much? Well, I also want to assume Compassion is honest enough that if you ask the right people about this, they'll tell you plainly what dropping out would and wouldn't mean to her.
Once you get that info you can better decide what to do.
In any case, it could hardly be a bad thing if you decide to keep up your support, despite some bad theology on their end, simply out of a concern for a less wealthy girl in some faraway land. Your instinct to not abandon her is a godly one.