IMHO if the entire family is C”Y then no, it should not be eaten (exception being if outside and there is no choice). It is hypocritical to preach one thing and then not do it, and is not good for chinuch bonim. Just my thoughts. And I am not C”Y. Would you give them unkosher food just because they are children? To someone who is strictly C”Y, C”ST food is almost like tarfus. At least, that is the impression I have gotten in the CR during the discussions.
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