I apologize, but I think your question needs a bit of clarification. A uniform doesnt preclude the use of armor. I mean, these men are obviously in uniform, but that uniform includes plate armor.
The practice of uniformly outfitting an army in the same matching attire is quite old, at least back into ancient Rome and Carthage. Officers would have a specific uniform compared to the main body of the force etc.
If you just mean when did they stop wearing armor, soldiers still do wear armor, and they never really stopped.
Even during the age of gunpowder, cuirassiers still wore a breastplate, as did Polish Hussars and German Reiters. Infantry gradually lost a standardized metal armor, but even up into the American Civil War and the World Wars soldiers were bringing steel plates to wear as protection. Metal helmets are also definitely a form of armor designed to reduce casualties from shrapnel.
Armor is ultimately a balance of how much protection is needed vs. how much weight and cost it will add. As offense (firearms) became better through the 18th century, armor fell out of favor. You could perhaps survive while wearing a steel plate, but how expensive was the armor, and how much would it really protect you, and how uncomfortable/tiring would it be to wear?
Of course, soldiers today are still heavily armored, just in ceramic plates and kevlar type materials rather than metal. The general infantry weapon today is actually less effective at penetrating armor than it was during world war 2 for the most part. so armor technology has finally "caught up" with penetration from firearms.
hi! there was a post on this yesterday: check it out for a summary by /u/elos_ and links to many other posts
