In both TNG and DS9, surgical gowns were used. These gowns covered the wearer's entire body, with the exception of the face. They never go into why they wear the gowns, but it is assumed that it is for cleanliness.
Now, it would make sense that the Doctor has no need to wear a surgical gown, as he cannot have any microbes, etc. But on multiple occasions, he has a nurse/medic assisting him, who has not been scrubbed, and is not wearing a surgical gown.
Now, you could make the argument that VOY has more advanced medicine. However, medicine on VOY is paused, if you will, due to the separation of Voyager from the rest of the Federation. That, and it plays at the same time as DS9, which DID use surgical gowns.
Is there an in-universe answer? If not, best guess?