We have been in a public school based Cub Scout Pack for 4 years. During this time I have been the Den Leader of my son's den. The pack meets at a church.
I believe Boy Scouts and Girl Scouts function in the same structure. A church may hold the charter for the group meeting there but frequently that is the only affiliation they have together. In our pack, we have all walks of life present from Muslims to evangelical Christians. Our charter is held by a presbytarian church. Our pack does do nice things for the church (i.e. plant flowerbeds, etc) but that is for the privilidge of allowing us to use their facility free of charge.
Now in answer to the public school aspect... In my experience (which is limited to our pack), things were fine when ds was a tiger (first grade) but things have gotten challenging as the years have advanced. The boys have just completed 4th grade. There is a definate difference in the "worldly" knowledge of the public schoolers and the home schoolers. There was not in the beginning but each year you could see the difference increase. Also, the lack of parenting (I am not saying that all public school parents are lax but my den parents are) is taking it's toll. The boys will mouth back, swear, and just be cruel. I frequently see the exact ill behavior of the boys in the parents.
I would suggest visiting a few troops. See how the leadership is. I would not worry about it being a church or school organization. Actually one benefit of having it outside a public building (i.e. a school) is that usually they give you a place to store some stuff.
Hope this helps...
Kathy