What does "religious exemption" really mean? What religious reasons do you need?
Well, this is very simple. You can belong to ANY religion and still use a religious exemption. A "religious" reason is essentially. ALL religions teach not to harm others, so if you believe that vaccines cause more harm than good, they would clearly be a violation of your faiths teaching against harming others. In reality, it's that simple. Your child's school doesn't have the right to question your beliefs or in fact even ask what religion you are.
In some states however you may be asked to have a member of clergy sign paperwork which reinforces your claim. This can be handled one of two ways, actually talk to your religious leader (whoever that is) or you have the option of becoming ordained yourself. The Universal Life Church (http://www.themonastery.org/) offers free online ordination and you can order all your paperwork (for proof) for just $27.
In most states however, you will simply need to state that it's against your beliefs and that's that. I suggest you take a few hours and research your states exemption laws before heading to your child's school for registration. This way you can have all your ducks in a row before you go.
If you have questions, there are a million "No-Vax" groups online. On Facebook I recommend the Choosing Not To Vaccinate group. But there are a great many others if you aren't on Facebook. Don't ever be afraid to ask questions in these groups, that's why they're there.