Snopes was right. It does get much more anti-God and anti-the Church in the second book. I would not reccommend this book to young children for multiple reasons, though it is compelling reading and I quite enjoyed it.
After successfully bridging between multiple worlds, Lord Asriel (the one with the black magick name) sets about to make war on God, or the Authority. Though it is breifly mentioned that this man has never been at ease with the Church doctrines, ("sacraments, and atonement, and redemption, and suchlike") others who join with him seem to be against what has been done by the Church in the name of God (intercision, which is essentially separating the souls of children from their bodies, thus killing many; male and female castration (mentioned very breifly) of children; and similar horrible things) "That is what the Church does, and every church is the same: control, destroy, obliterate every good feeling."
Therefore, they are determined to start again the war in heaven that Satan lost, and win.
That alone would be cause for concern to parents. But the God that Pullman describes is not a God that I know. If he indeed authorized and endorsed the actions of the Church, he is not a God that I would worship. Instead of turning me against God however, it made me remember how lucky I am to know about the true nature of God, that He is our Heavenly Father who loves us and wants us to be happy. He does not want to "obliterate every good feeling" but wants us to be free of the vices of the world so that we can enjoy true happiness.
Instead of making me despise the Church, it reemphasized for me the need for the restoration, so that we could truly understand the nature of God. It made me realize how much others are missing, and want to shout the truth from the rooftops.
I could see easily though, how one who does not have a testimony of the nature of God and their relationship with him could be swayed if they took the fantasy and tried to apply it in their life.