Some units did. If memory serves, most Marine units around the DMZ were required to wear body armor, but it was more a question of unit policy during that war. In some units only the point man wore a vest, while in others no one did and just down the road you'd find a company where everyone wore the flak jacket and helmet anytime they left the wire.
The Marine examples were from '67-'68 or '69, and they did foot patrols.
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