What school activities are there that you don't allow? Why?
At ten years old, there should be nothing at school that your child could be corrupted by as far as school facilitated/sanctioned activities. The only thing I can think of that Christians would be opposed to would be dancing/cheerleading, and many Christians are OK with that within reason. But at the age of ten, other than some dance lessons in P.E. I don't know that it would be an issue at this point either.
Now, simply being in school can introduce them to behaviors and attitudes from other children that aren't appropriate, but that is just life and can't be avoided.
By isolating your children instead of teaching them how to deal with choices and undesired behaviors from others, you are crippling them in their social and moral development. They will not have coping skills as early as others, and will not be as good at decision making. They will likely either live in fear and avoidance, or rebel and go the opposite extreme of what you are wanting. Being "in the world, but not of it" does actually require being part of society. You can't be in it, and not interact with others. The choice to participate should not be in question. The question should be what behaviors within the participation are acceptable.
