Cloud's coldly dismissive behavior and Empathy issues are keys signs of a particular mental disorder, that being disassociation, which Cloud not only has due to his identity issues, but is also drastically exaggerated because of his Mako experiments giving him Zack's memories.
Yuffie is the first and quickest one to welcome Vincent into the group despite his Nightmare Fuel Station Attendant tendencies. Of course she would be, both her and Vincent are an Optional Party Member in the game proper who can be skipped, potentially for the entire game but were made fully canon due to their popularity. Not to mention that in Dirge of Cerberus it's shown that Yuffie seems to be the most concerned for Vincent and determined to keep being his friend.
In a similar vein, this troper used to be confused why Aerith was so much more willing to let characters like Cait Sith and Vincent join the party than she was with Yuffie. And then it hit me- the difference is Yuffie is a girl, and thus a possible competitor to Cloud's affection. Heck, Yuffie even kisses Cloud if they go on their date in the main game. Aerith doesn't want her to join so she can keep Cloud to herself.
When Aerith and Yuffie first hear Vincent's "special" way of saying Hojo's name, Aerith first suspects that it was a Zombie, and Yuffie argues that it sounded like a Werewolf. One of Vincent's transformations is a werewolf like creature, and two are based off popular zombies in horror (Frankenstein and Jason Voorhees). And Aerith is ultimately correct, as Vincent really is a reanimated corpse who's retained his intelligence and memories.
Aerith's Clingy Jealous Girl traits have some basis in canon. The mechanics that determine who Cloud goes on a date with at the Gold Saucer come from his relationship with each girl (and Barret) and while Aerith starts the highest, her score is most likely to go down any time Cloud talks about/to another girlnote For example, if Cloud isn't chosen as Don Corneo's date, telling Tifa they have to go save Aerith improves Tifa's score but telling Aerith they have to go save Tifa decreases Aerith's score.
When the party travels on the world map, Aerith's portrait is positioned to be at the center of the square formed by everyone's portraits, probably to emphasize her status as The Heart of the group. When she dies in Episode 25, the space is left empty to emphasize the hole she left behind.