First, you have to consider who Abelas is and how he acts.
1, Abelas is a servant of Mythal and bound to her. So as Solas says, everything he does is guided by Mythal whether he knows it or not.
2. Abelas is very reasonable when dealing with reasonable shems. He wouldn't make an alliance otherwise.
3.The "not my People" comment has to be based on some sort of experience with the Dalish. I have a feeling that Abelas has been awake more than the other sentinels. Why? Because Abelas speaks the modern common language. The only other sentinel we deal with in the Temple doesn't speak a word of the modern language, but Abelas is fluent in it. I think this means Abelas must have made some sort of attempt at contact with the outside world, maybe even more than once, and like Solas was treated like a madman.
4. He doesn't mind teaching ones who don't understand what was lost. He has continued to teach younger elves in Mythal's Temple even though they don't even quite understand what Mythal was in all her glory and stuff. He even explains what the Well of Sorrows is to the Inquisitor even though he's not even sure that a mortal can handle it.
5. Abelas has absolutely no problem dropping truth bombs and he isn't even cryptic about it. Fen"harel locked all the gods away? Nope, Mythal was murdered and Fen'Harel and nothing to do with. This was history shattering news for a anyone in modern Thedas who knew anything about Elven lore and Abelas just drops that bomb like it was nothing. He also has no problem telling the Inquisitor when they first meet what they are and what they are doing. A huge difference between him and Solas is Abelas has zero reason as far as we know to hide who and what he is. Maybe in regarding current events he might feel hesitant to say anything if it would mess with Mythal's plan, but as far as the past is concerned Abelas seems to say whatever the truth is without hesitating.
6. Abelas is tired of his current life. He says it himself that uthenera would be kind.
7. This part is going to be heavy, heavy on some speculation by I actually think that Abelas had no idea who Solas was even an ancient elf until the exchange "Elven such as you?" "Yes, elven such as I."(This two line exchange alone is really interesting and can be analyzed on its own) His entire demeanor changes after this exchange from defensive to opening up slightly and relaxing. Just the idea that "Hey, these folks are running around with one of my People so they can't be totally bad".
8. And lastly, you have to consider the fact that who the Inquisitor is and what Abelas knows about them when he meets them at the Temple. The Inquisitor is some shem-elf running around ancient magic and chasing an ancient darkspawn through their lands and into their Temple. He probably doesn't know the full scale of what is going on in the world yet and how the Inquisitor is being treated like a modern day god complete with her own temple at the place where the sky is held up. The Inquisitor is a bit of a nobody as far s Abelas would be concerned from what we can tell.
Now, let's fast forward to let's just say two years and the chance that Abelas would meet the Inquisitor again. Some big things have happened that I think would heavily sway Abelas in the direction of at least becoming friends with the Inquisitor.
1. I don't know about you guys, but Mythal liked my Inquisitor. Said she was young, vibrant and did the People proud. This happened after meeting Abelas and since it seems from post game info that the spirit wisp of Mythal is still around, that means that without even knowing why Abelas(if still bound to Mythal) would have almost an instinctual respect for the Inquisitor he didn't have before. Even if he is not bound to Mythal anymore, the moment any mention of meeting Mythal would come up that would surely peak his interest. He worshiped Mythal for thousands of years and clearly loved her or something. he named himself sorrow when she died. So, this is a huge sway either way.
2. Quizzy has been up to some serious world saving stuff. She has defeated Cory, sealed the Breach,(Descent and JoH spoilers)
. These are all feats that earn respect and show she is not just some shem-elf running a muck in the forest.
3. Also, if after a second meeting Abelas found something worthy of following I think he would. Quizzy, like I said, has become like a modern day elven god walking the face of Thedas. I also think that if Abelas found anything that gave him even the slightest bit of feeling of real happiness he might make a hard turn and just run with it. 2000 years of being sad with some serious, forever looking worse job is a looooooong time. If Quizzy even caused him to crack one honest smile or laugh I bet he'd like her even just a little. And doesn't even have to be romantic.
So, yeah.....I think given certain things Abelas would be a lot more willing to chill with Quizzy post game.