Suppose my religion prohibits me from paying taxes? Or requires that wedding guests shoot up the sky with AK-47s? Or that I beat with a club any female who bares her face in public? Or that I must stone to death any woman who reports a rape?
The first amendment protects the free exercise of religion, but not does not allow violation of the law. Believe what you want, cast all the spells you like, kneel and daydream. Burn candles and incense if you like, but don't violate the fire code.
The government has the right to prohibit imports it does not want, for example monkey meat and black tar heroin.
If she wants to eat wild meat in New York City, there are more rats and pigeons than she could eat in a lifetime, so let her have at them.
What kind of religion is it anyway, that fails to recognize (or rather, completely ignores) the question of safety of fellow human beings? So typical of religions! When will we realize that we are better off without them?
This is such a shabby case. But it does bring to mind the Christian Scientists who refuse medicine to practice their so-called "medicine." It's a slippery slope that we try to walk on when we work to accomodate liberty. I think, though, that this becomes a utilitarian issue of health creating the greatest happiness.
We've been through this before with the peyote cult in the Southwest. Fundamentally, the conclusion is that you have to enforce the laws of the nation. If the consensus is that an adjustment should be made, then it should be made by amending the laws. We have many stupid laws, but I don't think this is one of them. There is no way we are going to accept such barbaric practices as Female Genital Mutilation or the ritual slaughter of traveling salesmen as practiced by the Thugee murder cult.
The precise rules are the topic for many a PhD dissertation, but the principles for valid laws are simple. For a law to be valid:
1) The law must not be intended to hinder or aid a religion. The classic example is laws regarding the sacrifice of goats and chickens. These were designed to interfere with the practice of Santeria. They did not interfere with killing goats or chickens as part of farming, veterinary activity, slaughtering, or butchering. This made it clear that they were religiously motivated laws. Had the laws made it illegal for those other activities to kill goats and chickens the laws might have stood, but the truth was that they were written to interfere with Santeria. The public did not want to criminalize eating chicken.
2) The law must be for a legitimate governmental purpose. This particular example might fail that test. Is bushmeat illegal because it poses a public health hazard? or because of endangered species considerations? Those are well established governmental purposes. Or is the law because of an "Eewww, that's gross" attitude towards eating those animals. That is not a legitimate governmental purpose. I don't know the facts in this case, so I don't know how that principle would apply here.
3) The law must be the least restrictive practical method for achieving its purpose. This is an area where there is endless legal debate and argument, and it is a constantly changing boundary.