I agree with a lot of this (especially the whole not everyone will know the words thing) but I would just like to respond with a couple of points.
The game is set in a stereotypical-fantasy medieval time. At this time in the real world singing as a lot more common in everyday life than it is today. All labour had to be done by animal or human because there is no other option. This leads to work songs, used to ensure that a bunch of separate people are working as one; sea shanties are a good example.
The Inquisition is a quasi-military. Two of its main founders are Seeker Cassandra and Commander Cullen. The military still uses songs, or rather chants, to keep soldiers moving in step (The old ‘I don’t know but I’ve been told’), each new batch of recruits is taught the old songs and organically makes up new ones (which leads me to my next point). This also goes for sports teams.
Again, back in medieval times, singing would be one of the very few forms of entertainment. Sure, on Theadas, the general level of literacy appears to be much higher than 14th century Europe but I will bet you any money that the peasantry still have a very strong oral tradition. People will make up songs about unpopular local lords, sing a few bars of that catchy tune the bard that came through last week was playing in the tavern etc.
The catchy-ness of songs has long been used by teachers. I can still remember the Tidy Up song I was taught in school when I was 4. I can also remember most of the words to all things bright and beautiful that I was taught at 7 and haven’t sung since. It would make sence that the Chantry would be running the schools out in the countryside and in the poorer parts of cities, so everybody who attended one (basically every single human from lower middle class on down) would be learning Chantry hymns. They wouldn’t have a choice.
Yes, the Dwarves and Elves might not know the words but we don’t know much about their actual religious practices, maybe they sing too. (I can guarantee you the Dalish sing. They have a solely oral tradition, they will sing. And Dwarves are miners and builders, they will have work songs.) And the thing is, the Chantry is so widespread and woven into human culture that if the song is a popular one the Dwarves/Elves might know it after all, simply by hearing it often.
Cullen having a lovely tenor? He was a Templar. Real world Templars were a monastic order as well as a military one. Maybe they have choirs?
Everybody having a trained voice is probably pushing it too far but if you go to school in Wales, you are taught to sing. From very young. Have you ever watched the Welsh rugby team? The whole team, and the fans, get really stuck into the anthem. All of the Celts are known to like a good sing song and at this point in the game a lot of the group are Fereldan.
There is also mob behaviour. Mother Giselle starts singing, the rest of the sisters join in, anybody who is particularly devout joins in (including Cullen and Cassandra), Leliana and any bards join in, soldiers see Cullen singing and join in. Soon you are going to feel weird for NOT singing.
tl;dr modern humans like you and me might get weirded out by spontaneous hymns but fantasy European peasants in a religion based proto-military would be much less likely to.
