At the end of the first map, Luke and Cory call out "NEW MAP!" Luke then stops and prompts Nat to join in, showing how he's already accepted the newbie as part of the group.
Luke asking Nat if she wants to see a movie with him after the Buggy Arc.
After teasing Phil a little, Luke comes up with the idea of Luffy knowing his father to make his entry into the group a little smoother. He also keeps commenting that Phil's fitting in just fine, welcoming him to the group despite how Phil's implicitly mocked their hobbies in the past.
GM lies about Phil's roll, letting him defeat Jango. It's a huge Pet the Dog moment and it probably factored in...
Phil's decision to join the group. He was making fun of them only hours before and by the end of the night he's happily joined the group. There isn't a big moment where he says it was a lot of fun or that he was wrong for being a jerk. He just joins without a second thought.
Cory upgrades his loyalty flaw to true Undying Loyalty, which the others warn means that Luffy (or more accurately, Luke) could outright tell Zoro to kill himself and Cory would have to allow it. Cory said he trusts Luke and upgrades the flaw anyway with a heartwarming in-character speech.
On top of that, everyone else rallying behind Luffy and Nami on the page after that. This goes double for Cory, who even up to that point wasn't sold on role-playing.
Usopp's repeated The So-Called Coward moments, such as when he deliberately goads Chu into fighting him so as to save his friends. The way Phil repeatedly declares how his cowardice gets outmatched by his desire to support and protect his crewmates is nothing short of beautiful.