Yes apparently you can duplicate relics by dropping them while garrisoning. Player colour or civ doesn’t seem to matter (tested with green and yellow, I thought the bug was for green players only, was Aztecs).
Steps:
Pick up relic with Monk.
Task monk to garrison the relic in Monastery (right click on Monastery).
While monk is walking to Monastery, task monk to drop the relic.
Monk will drop the relic, duplicating it, while continuing to walk towards Monastery and a relic will be garrisoned into Monastery as well.