do you think anne, based on her characterisation from the books, would, realistically speaking, be the voice of social change regarding issues like racism, homophobia etc the way she was in anne with an e? Obviously there's no occasion for her to do that in the books, but say she was facing a similar situation as in awae, would she stand up for these ideas (altho admittedly modern ones...) or would she reflect the "close minded" views of her time period?
I have never seen Anne with an E to any meaningful degree, so I'm not able to follow the comparison completely here because I don't know the specific plot point. I will quote this post which I consider brilliant, incredible, all the things, when it comes to Anne with an E's social issue approach. I'm also not sure I would describe these ideas as modern, but I do get what you're saying in connection with shows like awae, where it comes across as "character dialogue about social justice in the style of viral tweets where they do everything short of looking at the camera".
From a Doylist view, no. LM Montgomery was racist and homophobic, and although sometimes she seemed to question these social mores in text (the Japanese prince, her staunch dedication to more queerplatonic golden girls scenarios), she would have never written Anne like that to any meaningful degree. I think there is a case to be made for it to a very small degree, possibly, maybe, but I am skeptical. If you read her journals, you can get a sense of what she thought about these issues. I am specifically thinking of a passage where she learned an old school friend got an STD (iirc). She blasts him in a way I still think about because it was so dehumanizing. However, LMM's fiction did not always reflect her irl views. Cissy is a good example of that.
From a Watsonian level, it depends on which book we're talking about. AOGG features an Anne who frequently questions the status quo. Why do I have to pray to God? He made my hair red. Why do I have to go to church? I can just pray in nature. It's even lampooned in text by a character who is afraid to take the Sunday School class with Anne in it, because Anne asks such hard questions. Rilla of Ingleside and Anne of Ingleside feature an Anne who comes across as more traditional. Why are you spending money on a green hat, Rilla, when we need to make sacrifices?
Overall I don't think Anne could have ever stood for dehumanizing someone. Anne doesn't come across as someone who could generally stomach or stand for cruelty. Sometimes you get a waft of bitchy maud montgomery through Anne (thinking of the scene in one of the books where she goes to town criticizing everyone's appearance lmao), but in general, Anne is always searching for kindred spirits, even in what society might deem unlikely places. We also have Anne confronting her assumptions about people in different places in the text. For example, one short story involves Anne finding a journal of an older woman she had thought unpleasant and ugly, only for the journal to reveal the woman had a tragic past and a deep inner life.
I also think this touches on a larger debate regarding period dramas, where figures from the past are written to hold views seen as more modern (ie the infamous corset debate). IMO whether this approach works really depends on the story and genre. Some period dramas are meant to be accurate, and some are not really intended to be accurate at all (historical piece vs bodice ripper adaptation). When it comes to AOGG, to borrow a phrase from Anne Boyd Rioux, LM Montgomery uses an approach of empathetic realism, with an emphasis on empathy. There's death and grief, but it's offered with a tone of gentleness and hope.
How social change fits into that really depend on your individual interpretation. For example, with homophobia, disregarding LMM's intention, you could quite easily read Walter as gay, as the disapproval of him as homophobia, and the text as criticizing this disapproval and gender conformity. The story doesn't divorce Walter from his surroundings (realism) but it offers him understanding and love through friends and family (empathy). Applying that to Anne, I think a younger Anne would be much more likely to question why a social issue was the why it was - why can't she marry Diana, actually? - while stopping short of the twitter speech.
Moving back to the Doylist view, fun fact! LM Montgomery actually does this! albeit with much less controversial subjects. An LMM scholar has a wonderful quote about this that I cannot find, but LM Montgomery seemed to be fully aware of the power Anne held, and used that power to question social mores through Anne, the example being Anne questioning the goodness of God after Joy's death. That, or LM Montgomery straight up just writes the world she wants to. No one questions women going to college in Anne's world, besides a few one-off lines here and there. Women wanting education is presented as so natural it's not even a plot point.
I'll end by tagging @gogandmagog because I would love her thoughts from this if she ever rises from her tumblr sleep!