Liberalism is a mental illness.
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You don't know what their political ideology is. They homeschool and many homeschoolers are conservative. Some Conservative Christians practice holistic medicine (Amish to some extent). I'm a Vegetarian, but you'll be hard pressed to find anyone more, well I won't say Conservative, cuz Conservatism seems to be dead these days, but you know what i mean....
Veganism is probably unhealthy for children, pregnant mothers etc.. but I don't think vegetarianism is neccesarily unhealthy, although I wouldn't risk it with my wife or kids in that way.
In this case, I am actually leaning towards siding with the family over the state. I'd need more info to be sure though....
I'm siding towards the family as well, only because this isn't the first the CPS has insisted a person's lifestyle is dangerous for children and it turned out NOT to be. There's a family in Florida who had their children taken away based on their diet and then found out the reason why the baby died was because of a genetic defect.