No, Anne of Green Gables is too old (and too Victorian) to be a tale about young lesbians…even though (parents, this one's just for you) hundreds of femslash writers wish that Anne and Diana had ended up living happily ever after.
Ah, Diana. The pure devotion in the way Anne talks about her is sometimes laughable, because even though Anne speaks of her adoringly, telling Marilla "Don't you think Diana has got very soulful eyes?" (12.41) and referring to her as "my dear bosom friend." (25.52), the narrator shows us that Diana is no princess. She's a pretty normal girl.
When Anne offers Diana the wine she thinks is cordial, Diana drinks three tumblers of it—not really proper princess behavior. Diana's ordinary-ness is in her speech, too. When Anne uses flowery language, Diana responds with lines like:
"Why, I guess so." (12.28)
Anne loves Diana because she's beautiful and fashionable, qualities Anne wishes she had. It's not as if Anne tries to get to know Diana before asking her to swear to be best friends—she's in love with the idea of Diana. What actually makes Diana a good best friend, though, is her willingness to go along with all of Anne's schemes. A good leader needs followers, and Diana's perfect for the role. She may not come up with the most imaginative names for the natural wonders of Avonlea (or the best stories in story club), but she has fun and loves Anne's imagination.
Another reason Diana is good BFF material: she's loyalty personified. She's building Anne up, telling her that she looks good (since she knows how sensitive Anne is about her looks), reassuring her that her cake for the minister will be great, and reminding her of how well she's doing in school. So many people in Anne's life criticize her behavior, so it's cool that she has a friend who is pretty much always positive.
Diana isn't luckier than Anne in every way, though. She's limited by society. Her parents don't allow her to go to Queen's to pursue her teaching certification. So even though Anne's an orphan, she has more career options by the end of the book, while Diana can only become a housewife.