Cassandra tries to nudge Solas toward Andrasteism? Oh, good grief.
Not really. She asks him about what he believes in. He essentially says that he's a humanist. They discuss faith and the Maker. Cass says that Solas might derive some comfort from believing in the Maker, which prompts further discussion. I didn't see their discussions about faith as her trying to nudge him anywhere. She's a very devout person, yes. But she's discussing her own personal beliefs with someone who has expressed interest in them. Solas never says that his beliefs are incompatible with Andrastianism, or tells Cass to stop. In fact, he specifically says that he's always "open to new ideas".
As for her telling a Dalish Inquisitor that there might be room for "one more" if they talk about the Dalish gods, she's extending an olive branch to a person who she believes to be a very important religious figure, but who does not believe in her religion. It's also fairly early on in her friendship with the Inquisitor. I never saw that as overly pushy. I haven't done her romance, but I don't think she ever brings it up again. All of her talks about faith are, again, talking about her own personal beliefs.
Now, I can understand a pious Dalish not wanting to romance someone who believes they are an Andrastian religious icon. But I think that characterizing Cass as pushy about religion is doing her a disservice, and mischaracterizing her discussions with Solas.