Mollie leaves Animal Farm fairly early in the story, and her departure does not represent any ideological differences that she has with the chief advocates of the rebellion, Napoleon and Snowball. In fact, her character is depicted as fairly superficial; she does not appear to have deep ideological beliefs at all.
She leaves because she is a vain and silly character who only cares about wearing ribbons in the hair of her mane and having treats in the form of sugar rewards. The first thing she asks about life after the rebellion is whether there will still be sugar treats. She also does not want to sacrifice her ribbons.
The pigs explain to her that the ribbons are a sign of how humans objectify and demean her. The ribbons reduce her to the humans’s plaything or pet, in their view, and take away the free will she can have once Animal Farm is run by animals. However, she is not interested in hearing their reasoning. She misses the frilly way the ribbons twirl when she shakes her mane. She misses how colorful and pretty they are and how they make her feel pretty. Regardless of the opportunity for self-rule that the pigs preach will come after the rebellion, she wants to be under human care when she can preen and be coiffed and taken care of.
It is no coincidence that her name is “Mollie.” She wants to be mollycoddled or treated with an "excessive or absurd degree of indulgence and attention," as the Merriam-Webster dictionary explains. She represents a certain type of individual for whom independence is not appealing. The pigs believe that the ribbons infantilize her, but she does not care. She is not willing to give them up or give up the sugar cube treats.