This is hardly a major plank of his general argument (critics hunt around for excuses for attack), but, for the record, his point about labelling children applies to all religions.

As for the 'purity' part I note that Dawkins seems at pains to also make arguments against moderate believers who support secularism, and seems to feel that grave injustices are being done when a six year old visits a generic Catholic nun once a week.

But that is how it appears to me. It may just be a set of happy little accidents.