Wearing a shirt is not necessary for boxing, at any stage. If you mean Amateur Boxing, according to this page it says you have to wear it.. Head gear and regular groin protection are used as well.
"Competitors wear protective headgear and gloves with a white strip across the knuckle. A punch is considered a scoring punch only when the boxers connect with the white portion of the gloves. Each punch that lands on the head or torso is awarded a point. A referee monitors the fight to ensure that competitors use only legal blows"
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