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That those white circles with a red cross on it seen on ww2 medics' helmets were not standard issue. It was painted on by allied medics themselves after it became clear that

1. For the most part, the Germans respected the medics' role as a non-combatant and left them alone.
2. A lot of the medics that were shot was because that armband they had on one side wasn't very visible to the enemy. ("Fun" fact: most medics who were shot got hit on the side that didn't have the armband, further indicating that it was an identification issue)

So allied medics in the european theatre did everything they could to make their status as visible as possible. In the beginning they were unarmed, but for self defense purposes they began to lightly arm themselves with a weapon that didn't hinder them in their medical primary duties, such as with an m1911 or an m1 carbine.

In the pacific theatre it was the opposite: The japanese specifically targeted the medics, so there it was common for the medics to look like any other infantryman.