FYI, I had problems adding relics to a monastery, both as the English and the French, so it’s not an English-only issue.
Turns out that if you right-click on the monastery while carrying the relic, it gets added. You then see an icon for the relic, and the bonus accumulating.
I think the confusing part was that the tooltip said to left-click on the target (monastery), but that seems to just drop the relic instead of adding it.