Not my parents, no. But I found an article about it. Apparently the dog-tags for kids era was post WWII in the 1950s.
In February of 1952 the city of New York bought 2.5 million dog tags. By April of that year, just about every kid in the city from kindergarten to fourth grade had a tag with their name on it. Kids in many other cities like San Francisco, Seattle, Las Veagas and Philadelphia also got dog tags, allowing for easy identification should the unthinkable occur.
But educators weren’t considering just dog tags to identify the scores of dead and injured children that would result if the cold war suddenly turned hot. They also considered tattoos...
https://paleofuture.com/blog/2013/5/20/that-time-american-school-kids-were-given-dog-tags-because-of-nukesSensationalist version
https://www.dailymail.co.uk/news/article-4776328/US-pupils-wore-dog-tags-ID-bodies-Cold-War.htmlNewsreel about issuing tags in San Fran
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