There's more to this story that what's in the OP link. The Alliance Defense Fund claims that this is a case of a parent's right being usurped on religious grounds, but the facts of the case say differently.
The girl's parents divorced shortly after she was born. Their custory agreement says that education decisions are the joint decision-making responsibility of both parents (in other words, decisions like this need the consent of both parents). According to the documents filed in the case, the girl's father wants his daughter to attend public schools so she will have more opportunities to socialize with children her age, while her mother wants to continue homeschooling her. Since they can't reach a decision, they have taken the case to family court. A guardian ad litem was appointed, and agreed that it was in the child's best interest to attend school with other kids rather than be homeschooled.
If the parents didn't want a court to make the decision, then they should have reached a decision between themselves. Just because the mother is a woman of faith, that doesn't make the father's position less valid.
I myself don't believe the mother has the daughter's best interest in mind. This is based on the fact that, after their divorce, she moved her daughter out of state, away from the father. When parents divorce, they owe it to the children to remain geographically close to the absent parent so the child can have a relationship with both parents. I suspect that the mother is simpyl using her religious belilefs as an excuse for not getting the desired outcome in court.
If this were truly a simple case of a parent being denies parent rights based solely or primarily on religious beliefs, I'd favor the mother 100%.