Utterly blown away, yes. In Your Heart Shall Burn is fantastic from start to finish, and as a whole it is probably the most intense, gripping and touching sequence of story developments in any game I have ever played, a real accomplishment that everyone involved should be rightly proud of. I stopped after reaching Skyhold in the wee hours this morning, and while I hope the game still holds more awesomeness, this alone was more than worth the purchase.
As someone who usually doesn't care much for graphics, I've been particularly amazed by some of the facial expressions in this game and how they convey mood or meaning. Solas is especially good at that, a hint of a smile from Cassandra (or Leliana but geez she's closed off these days) warms me to the bone, and Cullen's expressions during the song were just incredible. It's a great example of how technical progress should support storytelling, not drown it out in ever more realistically flashy "bang!"s and "boom!"s.
I thought it was a rather touching and enjoyed it. I may not personally be religious, but even I felt that after what happened in Haven, it was a moment of much-needed inspiration and comfort for a group of people who had just suffered a major blow and who had probably lost friends and even family during the attack. Even if you dislike it, I figure that if you're a halfway decent leader, you can put up with singing you detest if it actually benefits your army's morale (in my case, I found it beautiful).
Seconded. Anyone who thinks being a leader means you get to trample all over what those "below" you think and feel and need is nothing but an abuser and a tyrant. I'm an atheist IRL and very very wary at best of most religions, but I try to roleplay my first/canon Inquisitor as a devout-if-troubled Andrastian because it makes sense given her background and the setting as a whole. It's quite enjoyable, occasionally challenging, and sometimes -- like in this scene -- also deeply touching. And hell, it's not like they're screaming fascist slogans or burning crosses on someone's lawn. It's just a song about sorrow and hope, started and shared in the spirit of coming together in a time of terrible loss and despair, a much-needed outlet for all the emotions that these people feel and a way to transform these feelings into something positive so that they may find the strength to carry on. There aren't even any in-your-face religious references in it.
Both my character and I find the kneeling and such a bit squicky, but if that is what people need in that moment, she'll put up with it. On the scale of "unpleasant things to do in order to help others", it doesn't even remotely compare to having the crap kicked out of her as almost-certainly-doomed bait for the Elder One. She survived that, so she can survive being called Your Worship now and then. 
Now the fact that the singing scene plays out the same way doesn't mean you have no agency. You clearly get to say exactly what you want - it's just that Mother Giselle has every right to ignore you and to do what she thinks is right in that moment. Like in real life, sometimes people will just do things that you don't want them to do, no matter what you say.
Full agreement. Player agency is crucial for computer game stories or we may as well read a book, but it should never come at the cost of other characters or the integrity of the setting. It's like player character power -- many (most?) gamers like a powertrip, like being special and whatnot, but when that "power" and "importance" comes partly from having all NPC authorities portrayed as lazy, uncaring, stupid, corrupt or inexplicably kowtowing to my every whim, that is just lazy, shitty and immersion-breaking.
Agency and power are both meaningless when you're surrounded by mindless, useless, ass-licking robots. I want to have choices and convictions for my own character, AND I want NPCs who have choices and convictions of their own. I want my character to be competent and respected for it, AND I want competent, rightfully respected NPCs around me as both allies and enemies. It'd be ridiculous to always have everything go our way.