I have NO idea if this makes sense or if I heard the theory somewhere else before but I like the idea that casteless dwarves are the descendants of mage dwarves (or those who preceded the dwarves...?)

The Shaperate is known to modify history and ultimately the memory of their society. The dwarves honestly don't seem to have a great grasp on their history despite being so obsessed with ancestors, seeing how Bartrand reacted to the very old non-dwarfy-looking dwarven ruin in DA2. The casteless in this case being the modern descendants of a theoretically-disgraced-and-reviled mage dwarf caste.

Obviously the idea of mage dwarves and their previous Fade connection isn't the unlikely theory and has been basically confirmed at this point just me being like AND WHAT OF THE CASTELESS DWARVES?? is the off the rails part lol