Forgive me for joining the conversation so late, but what exactly are we trying to discover here? Is it whether a parent has the right to label their child such and such or whether the labeling of a thing, person, or otherwise makes them what the label dictates? I can call myself a Catholic, Christian, or democrat, believe it, but not follow the precepts of such a label. Am I truly what I say I am? It seems only God can judge one’s heart in this matter, likewise we can’t know if our child becomes, or is, what we say they are by a label we give them. However, as a parent and guardian, enfolding the child into the family unit by its nature of being a child, it is perfectly acceptable to include it within the religion or political association of the family, regardless of their insufficient ability to believe or reason. When the child comes of age and reason to form or adopt their own system of belief they can label themselves and disown the ones of their childhood.
I think Dawkins falsely assumes an autonomous individualism of the child. Though a distinct person, the child is a part of the family body, as Christ is a distinct person, He is also distinctly a part of the Trinity and is God. The child assumes the label of the family not because the parent holds those beliefs but because the family as a whole is encompassed within that belief system.
I also think it is a non sequitur to say it is an “insult to their personal dignity” to label. An insult would infer a value judgment was being made. A negative label is insulting, some labels can be inherently positive, others relative to ones views on the labels connotation.