Saix only sees a puppet when he looks at Xion. No gender, no characteristics, not even a face. Number XIV is a sexless doll with a vaguely feminine voice (or at least Saix tells himself that it is to justify to himself why Axel refers to Xion as 'she').
Xemnas sees a boy when he looks at Xion. A specific boy—Sora. It's almost amusing, he thinks. They are trying so hard to keep Sora asleep and at bay and then they have a member walking around taking on the keyblade master's appearance. Of course, Xemnas knows that he is probably the only one who sees Sora in Xion.
Xigbar too sees a boy when he looks at Xion. Not the same one Xemnas sees, no, Xigbar sees a blast from the past instead. As if it wasn't enough that Roxas looks like he could be Ventus' twin brother. As if he needs two blond keyblade wielders staring at him as though he's drowned their goldfish.
Riku sees a girl when he looks at Xion. And not just any girl, no. He sees Kairi. He thinks it's cruel. How can he tell an innocent girl who looks just like one of his best friends that she has to sacrifice her existence for a boy she's never met? It would've been difficult enough if Xion had been just any girl, but when she looks at him with Kairi's eyes he cannot bring himself to force her back to Sora. She will have to make the decision herself and he can only hope that she will make the right one.
Xion sees a girl when she looks in the mirror. It is difficult to accept that not everyone sees her blue eyes and black hair when they look at her, that her apperance shifts based on the viewer. That to some she's a boy, or a different girl or just a puppet.
But Roxas never questions her identity and Axel tells her that she is no puppet in his eyes and she realises that it doesn't matter what anyone else sees.
Roxas and Axel see a best friend when they look at Xion. They see her as she is, as her own, unique person. Not a puppet, not someone connected to her replica heart and her false memories. To them she is only Xion—not Number XIV, not Sora, not Ventus, not Kairi.
Just Xion.
A girl with black hair and blue eyes, the same girl who smiles back at her in the mirror.