I don't think any of them is truly depicted as progressive in the political or social sense indeed, not even Dumbledore. The mere hints of social progress at the end is that it seems Witches in non-traditional roles might appear more post series.

Wizards at the forefront among the "good guys" are more depicted as "free spirits", unconventional, excentric and "anti-establishment", but still in a very traditional British (and even almost Dickensian) way, and still living in a very old fashioned world, and even regressive by their anti-modernism, or their lack of any interest in the outside modern society. For some reason I always thought she inspired herself a bit from the likes of Oscar Wilde and David Bowie. Whatever we know of Rowling's pretty left-leaning politics, the series itself wasn't quite a showcase for them. In fact it's mostly in her humourous caricature of the most narrow-minded brand of conservatism and later her growing attacks on the extreme right/left (all ideologies. Her most virulent attack on conservatives was perhaps with characters like Percy) that you could sense where she stood herself (though we didn't have much to guess, she was not secretive in interviews).

But in the end, she simply showcased certain traditional, consensual values of the European and British left (and classic right) through the series, mostly ethical ones like acceptance of differences, anti-racism/xenophobia, freedom of thought, and just as consensual woes of the extreme right and left, modelling her villains on Nazi/Stalinian models. She didn't go anywhere near socialist values and such, which isn't surprising and very coherent with her messages about propaganda, ideologies, doctrines, brainwashing and, basically, the perils of not thinking for yourself etc. With a message like that, she would have been in a very bad spot to pass her own political values in the series, or turn it all into an apology of progressive values. She navigated straight between the likes of Pullman and C.S. Lewis. Even then, she got heavily criticized by the moral right (who somehow decided wrongly she was a kind of Pullman passing atheist values to children), especially in the USA, and considering her highly moral, even wholly christian ending, it turned out they really missed a chance to shut up and wait to get the whole tale before attacking her.

She had a few social messages about wealth and poverty, but it was fairly restrained.

I think it's probably an indirect result of her decision to avoid passing to the kids a personal political agenda (and thus doing what she denounced), beyond (fairly) consensual values (except among the more extreme moral conservatives who see the devil in everything anyway). The global message is be yourself, don't blindly take as true or good what you're being taught by authorities and always keep your critical mind sharp, embrace differences etc.

She wasn't even critical of conservative values, confined most of her adult female characters to traditional roles like mothers, nurses, teachers (with rare exceptions like Tonks) etc. One of her strongest female characters is a stay-at-home mother who's almost a model old style Irish catholic mom. Her most progressive/controversial element, Dumbledore being gay, was mostly a read-between-the-lines thing (or would have been, without the interviews).

Yes, most fantasy works are extremely conservative in that sense, especially the ones who emulated Tolkien. In many ways, they're an ode to conservatism.. holding on, restoring or saving a golden age civilization attacked by changes, depicted almost systematically as evil. Even WOT was almost the American experience in reverse, starting with an idealized democratic utopia and a world of infinite progress returning after a cataclysm to far more primitive, harsher ways, and monarchies and old European style conflicts. Most of its heroes are models of traditional American values. And it ends with a warning not to seek to recreate the idealized past but to create from scratch and with your own hands your own better world, which pretty much sums up the American experience (it even ends with the brewing problem that one side of the alliance rests on slavery and the other is determined to see it gone).