Reddit mentions of Not One Damsel in Distress: World Folktales for Strong Girls

I wasn't raised religious, so never had those issues, but my parents are feminists and read me The Paper Bag Princess (http://www.amazon.com/Paper-Bag-Princess-Annikin/dp/0920236251) and Not One Damsel In Distress, (http://www.amazon.com/Not-One-Damsel-Distress-Folktales/dp/0152020470) both of which I and my sisters loved. When they get older, Tamora Pierce has a bunch of fantasy books with female protagonists, and Diane Duane's So You Want To Be A Wizard books were also favorites.

Edit: How could I forget Madeline and Pippi?! https://www.buzzfeed.com/sarahbreen/feminist-books-ftw?utm_term=.hs2PoxVvj#.ug2KJ8X0B
Also Ella Enchanted is a great retelling of the Cinderella story, I think it's either Jane Yolen or Ursula K LeGuin

I'd say you could give them books by Dianna Wynne Jones Vivian Van Verde, Ursula LeGuin, or Jane Yolen.

but there's all kinds of folktakes and fairytales they might like with legitimately strong women and girls.