I admire the Boy Scouts so, but would NEVER be a Girl Scout for those very reasons!!
As it is, I right now belong to two girls’ clubs, both of which are Catholic. One is Little Flowers, which some of you may have heard of. It is run for the homeschool girls at our parish. Although it doesn’t really have a ministry, it’s designed to form the girls into good Catholics with our model as St. Therese. Thanks to our leaders, it’s also great fun!! It has expanded from a dozen or so members to over a hundred (this is an estimate) in less than 10 years!
The other club is run by one or two of the sisters at the convent near us. (So it, sorry to say, is very local, and not an option for all.) Its membership has also expanded rapidly; our ministry is mainly to help the sisters serve the meals at their Retreat House, because they are often drasticly shorthanded. We girls enjoy helping them, and they are very, VERY grateful for the help. (They also keep hoping that we’ll all end up postulants someday!

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Its really fun to help them; often we stay overnight and will participate in their Divine Office as well; that is a great experience.
So, I say, obviously DO NOT support the Girl Scouts and make them aware of your disapproval. Also, if your daughter wants to participate in a club, why don’t you start your own with her and a few of her friends, choosing an appropriate community service ministry?? Come on, you can do it!!!