In what circumstances does Solas say this?

Yes, I know what scene it is. I meant the different versions of its dialogue.

This is true. You need to take on the role with the "faith" option. You also need to embrace the title Herald of Andraste when talking with people like Mother Giselle and Cassandra.

You need to have low approval as well (significantly negative approval)but the OP was specifically asking how you get the dialogue "Do you enjoy the worship?" I don't think you get it if you have been constantly denying you are the Herald even if you have low approval. You have to have specifically founded the Inquisition on Faith. Otherwise you get an alternative caustic comment from him.

In order to get approval low enough, you have to constantly opt for choices in dialogue and decision making of which he does not approve. So constantly voice disapproval of mage freedom, his views of magic, ally with the Templars, approve of the Wardens and keep them with the Inquisition, refuse to help his friend or kill his friend if you do his personal quest, ally with the Qun. You get the general idea.

To be honest I think it must be quite an art getting his approval low enough because I did a lot of these things with one of my Inquisitors and he still thought he was a great guy. I'd helped his friend, though, and hadn't declared for Faith but I think my guy was just too chatty with him. Solas loves talking about himself and his experiences in the Fade, etc, so not engaging him in conversation about these things at least doesn't improve your approval even if it doesn't impact negatively.

In the Keep, it's impossible to not be friends with him and do his personal quest regardless of the result, which means that the quest and that cutscene are mutually exclusives. I don't know about receiving the quest and refusing to go there changes something.

I must admit I am assuming a bit here. You are right that your approval needs to be high enough to even be given his personal quest. That is the same for all the other characters too. I went through the first game never having been given the option of aligning with the Qun because I had never got Bull's approval high enough. Then I read on the boards that I should have been able to do that, so I went back, took him on a dragon hunt and, bingo, the series of dialogues that leads to that encounter triggered.

So if your approval is low, Solas' personal quest never triggers and you are probably well on your way to the negative approval dialogues.

What I was suggesting (and I may be wrong about this) was that your approval might be high enough to trigger the quest but then you could either refuse to do it or kill his friend and that would send your approval rating back down again. If the Keep doesn't allow for this scenario, then I assume I was wrong and even failing at his personal quest will not stop you from being considered his friend.

No kidding. I mean, a mage being in any position of political power (aside from court mage) was a big no-no for the South. So big that it was a big part of why the Imperial Chantry separated from the Andrastian Chantry. Which is to say nothing of the modern Chantry that nearly looses its shiz when a Circle potentially forms in Orzammar or if Ferelden tries to give its Circle autonomy.

But then, I suppose a mage becoming Divine is just as impossible as the Dalish being given thier own land in Ferelden or an elf being made Marquise of the Dales. But I suppose I can let it slide if her Divineship ends just as disastrously as would be expected.

To be fair that was about all Alistair/Anora could get away with. As it stands, the epilogues all but imply that whatever increased status the elves get, it eventually gets matched with heightened racial tensions or straight up deaths. The implication being that these choices are unmade or reverted back to state reminiscent of the status quo by the time the next games start. Which is unfortunate...but not unexpected. Or unrealistic.

In all probability Marquise Briala and Divine Vivienne may start out successful enough with thier gathered support, but that will not last forever. Hell, Vivienne almost immediately had to deal with open rebellion in most of her epilogues. In all likelihood, both will either be assassinated or removed from power. Or put in a position where they will be prevented from making any real change. Same goes for Leliana, unfortunately.

For all as much as we rail against the status quo, the world insists that it is unwilling to change to any large degree.