That's the problem. Laws shouldn't have religious exemptions. I'm not just talking about this law, I'm talking about any law. Or rather, no law should have a specifically religious exemption. Laws can have exemptions that include religious reasons, but they shouldn't be exclusive to religious reasons.
There are two reasons for this. One is that religious belief shouldn't be treated any differently than any other belief. If a religious conviction is enough to exempt you from a law, then a secular conviction should be as well. Otherwise you would be elevating religious beliefs above secular beliefs.
The second reason is that it violates the separation of church and state. You might not think so, since usually religious exemptions are intended to prevent laws from hindering the free exercise of religion. But that's the problem. It forces the government to decide what is or is not a valid religious belief to qualify for an exemption.
Not only does that violate separation of church and state, it does so in a way that is biased against minority religions. Members of major religions generally won't have any problems convincing a judge that their belief is sincere. Only members of small religions will have to worry about not being allowed to practice their religion freely, which seems like exactly the kind of thing that freedom of religion is supposed to prevent.
But what about free exercise of religion then? Well, generally laws are passed for reasons. If those reasons are good, they probably apply to everyone, religious and non. You can't murder people, even if you really truly believe that the god Huitzilopochtli needs them to make the sun rise.
If a religious exemption is really necessary, it can probably be rephrased to be secular, and still apply to the religious. For example, non-profit organizations are tax-exempt, whether they're churches or not. (Though current law more or less automatically gives religious organizations non-profit status, which is the kind of thing I'm arguing against here.)
And if that's not possible, maybe the law shouldn't be a law in the first place. If "I really truly believe in