One of the things that surprised me more when I role-played a Dalish Inquisitor was how respectful Cullen can be towards pagan characters. It's especially noticeable in Haven.
Cullen is a devout believer in the Maker, still follows the Chantry and it's evident he believes the Inquisitor is the Herald of Andraste, but he never judges or berates the PC for their religion, never expects them to share the same views, never tries to convert or convince them to change their ways. When the whole "Herald of Andraste" thing is mentioned for the first time, he's the one (the only one) to ask the PC about what they feel and is always more worried about the Inquisitor's safety than about any propaganda scheme. Him being totally okay with Dalish vows in the wedding is in character and the icing on the cake.
And it's not as if every other character was the same. Thankfully, Bioware provided many points of view. From Cassandra's "there's no room among your gods for one more?" to Mother Giselle trying (very kindly and politely) to convert you, from Sera breaking up with a Dalish Inquisitor that doesn't agree with her to the aforementioned Dalish vows in Cullen's wedding, from trying to deny being the Herald to embracing the role and judge in the name of the Maker, every character and every Inquisitor had their own opinion on the matter.
Yeah, I was rather surprised to learn that BioWare made the Tevinter Magister's son and Andrastian holy warriors (Cassandra, Cullen, and to a lesser extent Leliana) more accepting and open-minded about the Dalish than our two elven companions. I guess it was for some tastefully subtle message that sometimes people not part of an oppressed minority can be more sympathetic to your cause than fellow members of said minority (same with Bull to Adaar), but eh. To this day I'm still holding out for that "elfy" romance where said elven companion doesn't disavow all elven culture (the only elven companion thus far who doesn't distance themself from other elves is Merrill, and you can only romance her as a human 
), but it looks like I'll wait a long time yet.
For now, Solas and Cullen are awesome. Maybe it makes me a bad person, but my Dalish elves tend to prejudge Andrastian humans as intolerant of mages, elves, and pagans, especially Andrastian priests and Templars. One of the things I like about the Cullen romance is being able to headcanon my girl starting out distrusting him for being a former Templar, then getting to know him, learning how kind and open-minded he is, and learning to be more accepting and open-minded herself.
Some people take issue with his lyrium quest since it involves the PC "fixing" a love interest instead of you two supporting each other, but I don't think that's strictly true. Like you said, he's probably the only companion or adviser who asks how you're feeling and doesn't ever pressure you to live up to propaganda schemes, so you have his full and undivided military and moral support. (Even Dorian, the only other companion/adviser who asks how you're doing, still worries about your image--like how it would look for the Herald of Andraste to befriend a Tevinter mage like him.)
I'd like to think that Cullen helped free her from the mental bonds of subconscious prejudice by being kind and supportive, so she returned the favor by helping to free him from his lyrium leash by being kind and supportive. I like to head-canon that it was a trade-off, not a one-sided, "I fix you, then you reward me with sex."
That's true, there's a lot of room to interpret them having a lot of dream dates. 
Between the in-game ability for my character to talk to him any time at Haven or Skyhold and take him anywhere in the game, I imagine that my gal spent every waking moment she could with Solas, and then dreamed with him after she learned Fade-walking at Skyhold. I actually headcanon that they spent so much time together that she eventually became mentally exhausted--not from lack of sleep, but lack of being able to rest her brain since she was essentially "conscious" all the time. Eventually even Solas had to tell her that she needed rest... cue her taking a nap in the Fade by sleeping with her head propped up on his shoulders while they rest under a tree on a lovely summer's day.
Retour en haut
Really though that's the beauty of headcanon. Heck Ceru and I have sibling inquisitor headcanons 
It's safer not to make judgments about why people made the decisions they did. After all, it's a game, and even when people pick what appear to be the worse evil choices, they may have their reasons (even if it's to feel the pain of sacrificing their happiness...or they just want to see what happens.) 
