The serious point is that "free" states don't allow the practise of religion to stomp all over people's other rights. Freedom of religion is balanced with the other freedoms - in this case, you could argue, the anti-burqa crowd may be trying to argue that it impinges on other freedoms.

My advice would be to keep the state from exerting any power over people that isn't absolutely necessary

You're confusing necessary and the norm in the US. Why is it necessary that female nipples be covered but not male? Why is it necessary that penises must never be seen? Why is it necessary that polygamy be banned?