This presupposes two things: firstly, that soldiers wore beards before WWI, and secondly, that they shaved for convenience in the field. For the British Army, both are false.
In the years before WWI, moustaches were essentially required by regulations. The regulations in place in 1914 stated that
The hair of the head will be kept short. The chin and the lip will be shaved, but not the upper lip. Whiskers, if worn, will be of moderate length.
This meant that, for soldiers old enough to grow facial hair, they were wearing moustaches. In civilian life, however, being clean-shaven was already fashionable - some men got into trouble for shaving before leave. Holmes mentions an incident where two officers from the Accrington Pals, who had shaved before going on leave, were upbraided for their choice. The reservists and new volunteers had never paid much attention to the regulation in any case.
During the war, this regulation would change. During the summer of 1916, an officer was court-martialled for shaving his upper lip. In civilian life, he worked as an actor, and felt that growing a moustache risked a rash when he shaved it off at the end of the war, one which could jeopardise his ability to find work. This defence failed, but he was saved from being cashiered by the intervention of the adjutant general at GHQ, Lieutenant General Sir Nevil Macready. Macready was not a fan of his own moustache, and so quashed the sentence and had regulations changed to allow for the upper lip to be shaved. However, shaving in the trenches was not always practical. While the men did the best they could with razors and whatever hot water they could find (or even tea), many found it impossible to stay clean-shaven. Beards were, thus, not uncommon in the front line. In 1917, Joseph Maclean wrote, describing conditions in his trench, ‘I haven’t washed or shaved for a week and look like a Boche prisoner’. However, when they went out of the line, men found shaving to be an essential part of the process of cleaning themselves of the dirt of the trenches.
Source:
Tommy: The British Soldier On The Western Front 1914-1918, Richard Holmes, HarperCollins, 2004
I’m hoping that posting this isn’t against the rules, but said by whom? I’ve never heard this claim before, and it’s not as if renaissance art—depicting life well before the Great Wars—only features men with facial hair.