Great post and great discussion!
We're in CA and have been charter school participants for 7 years now.
Interestingly enough, our charter school calls us "homeschoolers"...despite whatever legally we are deemed. The teacher we work with calls herself a "homeschooling mom", and our local homeschool coop is made up of many charter school and non-charter school families.
We're are very small, rural community though, so we might do things a little different here. :)
I also wanted to mention that although our school will not purchase religious materials, they will allow me to include them on my learning records and as samples of learning.
AND, I have purchased MANY materials from classical publishers through our school, including many Susan Wise Bauer resources (Writing with Ease, SOTW, etc), and Greenleaf Press materials.
A few years ago, the school hired Andrew Pudewa to come and teach a seminar on writing for all their staff and parents, and since then, we've been using IEW materials almost exclusively for Language Arts. They school buys these materials for me. They also have trained instructors to teach IEW small group classes for their students. Way cool.