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It says it all.

Belle is often accused of being "snobbish" and "stuck up" for not interacting with the villagers, yet the film establishes that she desperately wants to talk and connect with people, but they won't let her. When the Baker says good morning, she turns around and says good morning right back. When he asks where she's off to, she excitedly tells him about the book shop and the book she's reading, only for him to say "That's nice," and focus on work. She shrugs and walks away, only for the town to gossip about her. No one says hello or comes up to talk to her, yet she's the snobby one??

The villagers blow her off and badmouth her behind her back. What is she supposed to do? It seems most of them don't want to discuss books or ideas, which Belle is very interested in. Most of them just talk briefly about their jobs, gossip about other people (which is itself snobby and stuck up), or just gush about Gaston. Belle is not interested in these things, and can't have meaningful conversations anyway since those topics are by their very nature brief, shallow, and unkind.

I've heard it said that Belle looks down on the villagers for not being as well-read as her. Yet, Belle makes it clear she doesn't hold them any ill will. When she comes home, she asks her father "Do you think I'm odd?" She doesn't consider herself the standard of excellency while everyone else is below it. She wonders if she's the one with the problem; the wrench in the machinery. She even says, "I'm not sure if I really fit in here. There's no one I can really talk to." Again, Belle doesn't say there's something wrong with the villagers. That they're ignorant or shallow. She feels that they're fine but perhaps she's the one that is off or doesn't fit in.

Lastly, Gaston. I've heard Belle accused of being shallow for calling him "positively primeval," "boorish" and "brainless." The problem is we see Belle being very polite to Gaston prior to his rude behavior. She addresses him as politely as anyone else in town when he drops in front of her, but only gets annoyed and impatient after he repeatedly takes her things, tells her what she should do and how she should think, and even invades her personal space by physically leading her toward the tavern even though she shows no interest. She only becomes insulted that he "asked her to marry him" after he becomes presumptuous enough to make himself at home in her house, presume she wants nothing more than to wait on him hand and foot and give him several "strapping boys like him," assume her answer is already yes, and presume that her avoidant and defensive actions are just her playing hard-to-get.