Anders' views on the Fade are different than how Solas views the Beyond, including their perception of spirits. Anders was a bit pushy, with his refusal to accept that she didn't view 'Spirits' and 'Demons' as the 'First Children of the Maker' and those who turned their backs on the Maker to embody 'different sins'; he was quite Andrastian, and seemed to have this inability to grasp that her cultural views gave her a very different perspective on the world, and the Beyond, than the one he held. Merrill disagreed with Anders' very black and white view of the denizens of the Beyond.
Solas is entirely different, in the sense that he shares his views on spirits and the Beyond with a curious Lavellan, and while he vocally agrees or disagrees with certain ideological actions (from the schism between the mages and templars to what the Inquisitor does with the Grey Wardens), he doesn't really seem to push his spiritual views on anyone in the same fashion that Anders did (although I can understand why, given the context of bringing the Chant to the four corners of the world, and all that).
I think Merrill would jump at the chance to pick Solas' brain about the past. What it was truly like, what discoveries he's made in the Beyond, what he's learned about spirits. To finally have someone who could answer those questions is something that I think would really peak her interest. Perhaps I'm somewhat biased because I expected to dislike Solas when I heard he was anti-Dalish, and found him to be a very intriguing character who ended up becoming a good friend worthy of my respect, so maybe I expect that she might have a similar reaction.
Merril believes too much in her own culture to have it torn down on the basis of "because I said so". She is Dalish through and through, she would come to Solas from a position of superiority because he is not (from her perspective) one of the People. She'd condescend to him much in the same way she does with Fenris. He comes with interesting information, sure, but he has no proof to back up his claims. Merril is too intelligent and believes too strongly in her people's lore to take him at face value or accept it simply because "he saw it in the Fade". She is inquisitive and she'd want to know where he found it, then she'd want to see his proof for herself. She bargained with the demon because it gave her what she needed to do what she wanted. For all that she's naive,she's also clever, intelligent, and talented. Her demon is Pride and one of the weapons you can find on her persona quest is Hubris, pride is her achilles heel. She and Solas make the same mistakes, which is pretty much why they'd never be able to stand each other.
Ultimately, the lies Solas tells would be the nail in the coffin of that relationship. His lies only stand up when they are taken at face value or simply accepted, ask too many questions about where he gets his information and it all comes tumbling down like a house of cards in a stiff breeze. He didn't create a good enough cover to withstand harsh scrutiny and the only reason he survives is because most of the characters consider him to be trustworthy. The ones that don't overlook him, including those who should know better. Either way, when people ask questions in Inquisition they aren't asking the right ones and they don't double check. It's how both Solas and Blackwall slide in under the radar. (Which is funny because there are enough holes in his story that both Leliana and Bull should be checking simply out of habit on the basis that they are spies and no one is trustworthy. Multiple characters do notice his inconsistencies, they just never press deeper.)
Eventually, he'd have to come clean and when he did she'd accuse him of trying to destroy her all along. It's the same fear he has about Lavellan, actually. Merill is also too trusting when it comes to spirits and she doesn't differentiate. While it never hurts to listen, Solas isn't a fan of walking in blindly when it comes to dealngs in the Fade. He wants us to trust him and his advice, not spirits in general. Merril knowingly making a deal with a pride demon and actively advocating for deals with others just because they offer would get in his craw, especially when it came to someone he was protecting/cared about. Imagine the encounter with Sloth or one of the other demons in 2 with Lavellan and Solas both there. Merrill advocates for Lavellan to trust and make a deal with the demon, depending on what the demon wanted he'd flip out.
They have just enough similarities to get along initially and then just enough differences to drive each other batty, which is why I actually brought up Anders. Anders and Aveline are both a great examples of what happens when anyone tries to tell Merrill what to do. She resents anyone disagreeing with her and she doesn't want to debate it. If anything, Solas would probably land himself in the same role as the Keeper, but without any of the Keeper's actual authority over her.