In fact, it's so nonsensical I'm beginning to think you purposely put it forward in that way just to see what sort of replies it would generate.
'Fess up now. You were just funnin', right?
Me? Post something outrageous just to get a response? How dare you say such a thing! Why that would be....the essense of blogging! Guilty as charged.
The argument still stands, and I've moved it up here, where I can spread out a bit. OK, it seems preposterous to allow a child to suffer and die, based on her parent's religious beliefs. But as I pointed out, absurdity is often codified into law, just as in the example I gave. Some of the charges against Richard Reid were dropped because the legal definition of mass transportation does not include passenger aircraft. Certainly this is an absurd reading of a statute, but the ruling will stand. Merely calling an interpretation absurd says nothing about its legal merit.
However, let's address your argument about doctors. You say that if my interpretation were correct, that doctors could choose to deny treatment to patients of certain faiths, based on their first amendment rights. This is not the case, even under my interpretation of the first amendment. Doctors are licensed by each state, not the federal government, and the state licensing process includes the requirement that doctors will treat all patients, regardless of race , creed, etc and so forth. In fact, licensed medical professionals are required to give treatment in emergency situations, even if they are not on call. Paramedics, for example, are required to stop to render first aid at the scene of an accident, even if they are off duty. (Of course, this is an unenforceable law, because if they didn't stop, nobody would ever know. But that is beside the point.)
There is no first amendment conflict here because nobody is required to become a doctor. They can choose not to agree to the conditions, and forgo licensing. If they choose to practice medicine, they voluntarily cede some of their first amendment protections, similar to the way folks entering the armed service cede some of their rights.
Now, let's look at the other side of the coin. If the state has the right to intervene in matters of religious faith, then what limits that right? You suggest that when the faith has the potential to cause damage to minors under the care of the practitioner, then the state has the right to intervene. Is it merely physical damage that allows the state to intervene, or can the state move in the event of emotional or psychological damage? Telling a child he is a sinner could certainly be considered as emotional abuse, yet that is a core element of most Christian faiths. Should that be grounds for state intervention? How about financial damages? If a parent is tithing heavily to a church, reducing the income available to support his child, should the state be able to intervene then? How about faiths which renounce worldly goods, requiring their members to give away all possessions and live a life of poverty? Should the state take their children away?
Let's look at things from the mother's point of view now. She believes that earthly life is small potatoes compared to heavenly life. She believes that what happens to our physical bodies is irrelevant, that our souls are what really matter. She believes that we must submit to God's will, and allow his plans to come to pass in our lives. These are standard Christian tenets, but she applies them to her life and her daughter's life with a rigor we cannot match. We profess as Christians to believe the same things as she does, but when we get ill, we don't turn to God, we turn to Marcus Welby, MD. My personal belief is that God helps those who help themselves, and that doctors and medicines are resources He put here for our benefit, but that's just me. Her faith and belief is different. Do I have the right to force her to live by my beliefs?
Finally, let's make a slight change in the case, and see if your reponse is any different. Suppose that, instead of faith, she had relied on some non-traditional treatment for her child. Instead chemo and radiation and surgery, suppose she had opted for a homeopathic therapy combined with nutritional supplements. These are not cancer treatments that are recognized by the medical community, in fact, the AMA is working to regulate those who practice these therapies out of existence. Does a parent have the right to chose which treatment she thinks is best for her child?