"I'm not a religious person and do not wish to participate in religious activities. It's against my beliefs."
If you're saying you're an atheist, the only thing that characterises us is that we don't believe in God. Anyway, wearing a cap doesn't mean you're participating, just that you're not being a dick.
Honestly, I think religion is infantile at best, but you aren't being asked to pray or have your foreskin cut off before you enter, so what difference does it make? Its such a non-issue you can't even claim its a matter of principle.
I was accepted to a 6th Form that was Catholic, but had mandatory prayer sessions about points during the term (in spite of them claiming the school was not only for Catholics), and so I went somewhere else on the principles that education and my religion (or lack thereof) should have nothing to do with each other, and that they were being hypocritical, and that I am against religious schools anyway. If I hadn't of had to do anything other than wear a specific article of clothing that didn't bear any relation to anything else anyway, I'd have probably considered it more.