I guess I don't really understand how keeping your child home during the testing because you're "against them in principle" accomplishes much of anything - if you're passionately against them, I think the way to accomplish something is via advocating, opening discussions with the school district, with state ed officials, organizing other parents etc. I can't imagine that not sending your child would accomplish much of anything other than annoying school staff that you want to have on your side for more important things you'll be advocating for.
But that's just me! Things might be very different where you are. Here, our state tests and how they are used is exactly as Dottie described, except that we don't have a religious exemption option

Best wishes,
polarbear