Well ... if the DM feels ambitious enough, each Cleric could be custom-built to match the dogma of the Diety they follow. But then you'd be entering the quagmire of 2.5 D&D ... where you could trade off Heavy Armour for better saves, or better BAB but less spells, etc.
I could be wrong but I think a lot of what we view as the 'Cleric' in RPG's was really the Fighting Bishop/Cardinal of the middle ages. They if they chose (if they were wealthy enough in spite of a presumed vow of poverty) could have a full suit of Maximillian plate, a holy water sprinkler-styled mace and shield. This weapon was brutally effective ... and honestly an exception to what most of the examples of a fighting religious person ... except for many of of the fighting monastic orders ... Templars, Hospitalers, etc.
But look at say the high priests of the Aztecs, the Sumerians, the Greeks, the Romans, the Wise Men of the Prairie Peoples of North America. Only the Europeans would have even been covered in steel from top to bottom ... the Aztecs would likely have had a hardwood club with Obsidian flakes wedged into it; the Sumerians may have had boiled leather armour and a khopesh or something similar; the Greeks with a bronze breastplate, greaves and bracers, a spear, club or sword; the Romans a bronze breastplate or something similar to that worn by a Centurion with weapons to match; the Wise Men of the Prairie ... buckskins, maybe a bone vest and a spear, bow or club.
So our view of all Clerics wearing plate, wielding maces and such is based on the culture they were from. D&D is unflinchingly euro-centric for the most part.
Summary: Clerics 'Can' wear Heavy Armour, they 'Can' wield a shield, they 'Should' have always been proficient in their Diety's chosen weapon, they 'Should wield, wear and be proficient' in armour, shields and weapons that fit their Diety/culture/setting. If your setting is Euro-Centric so should your expectations of gear ... if your game is not feel free to limit what gear is available.
