Last week, I came across this Tumblr post: Why Daenerys Should Not Be Glorified. In it, the author argues that Daenerys is a deeply problematic character in the series, because she acts as a White Savior in Essor, echoing themes of imperialism by storming into places like Astapor, inflicting her own moral beliefs on the people, and destroying the cities without any understanding of their culture.
It's an interesting read, and it makes some valid points. But I think it goes too far in condemning Daenerys and her savior complex.
Dany's story is neither an imperial narrative nor an anti-imperial narrative, but a story that (like many elements of A Song of Ice and Fire) falls uncomfortably in between.
(This post has vague book spoilers beyond what's been shown in the TV series)
Daenerys does play the role of the "white savior" in several of the books. In A Game of Thrones, she does nothing to stop Khal Drogo and his Khalasar from raping and murdering the people in the towns and villages they pass in general, but sets herself apart from them by trying to save whatever individuals she can. But although it has "white savior" implications, Dany is just playing the role of a decent human being here. It is perhaps problematic that the Dothraki are presented as a savage culture that do these sorts of things, but then again, their actions are mirrored in Westeros again and again, with Clegane's men, with the Brotherhood without Banners, and on and on. Dany is in a position of some power and influence (although nowhere near as much power and influence as she would like), and she attempts to use that power to save whoever she can.
And yet, she fails. As Mirri Maz Duur makes clear, she didn't actually "save" anybody. She tried to help some people, out of goodness, but that doesn't change the fact that she was part of the group that attacked her, and that saving someone's life isn't worth much when all the rest has been destroyed.
We see a similar problem in the third book. Daenerys liberates the slaves in Astapor and kills the masters in the process. As the tumblr post stated, this could be read as the white saviour coming in and saving these more barbaric cities from their wicked ways. After all, although many things are acceptable on Westeros, slavery is decidedly not, and there is something more than a little hypocritical about Daenerys accepting Jorah as an ally but killing these others involved in the slave trade without a thought.
But she's also being a decent human being, and using her power (and her dragons) to save thousands of people. I don't think it's wrong for Daenerys to "impose her values of right and wrong" on a slave city where thousands of people are suffering and dying. At a certain point, right is right and wrong is wrong, and Daenerys cannot be faulted for tricking the slavers and destroying their trade and the city it is built around. If she turned her back, that would open her to a different kind of criticism, of being too cold-hearted and not caring about anyone she's not connected with.
She can, however, be faulted for not thinking through the consequences of her actions. As a dramatic set piece at the end of an episode, Daenerys' liberation of Astapor was fantastic. As a long term strategy, it's all going to fall apart, as A Dance with Dragons shows. We cannot fault her for wanting to free the slaves. But she was naive to think that she could simply "liberate" them and that everything would be fine. If she's presented as a kind of imperialist savior, then the ensuing story acts as a criticism of that attitude, even if it's done with the best intentions. She swooped in with her dragons and "fixed" things... and in some ways, things became worse as a result. The change has to be internal, not made by force, in order to take hold.
I do think that the representation of non-Westerosi cultures and races is one of the most problematic elements of the series, especially as it ends up with the white Daenerys providing a kind of moral intervention in Essos (even though some of the things she intervenes with are also seen in Westeros, and her interventions usually fail). Yet Daenerys is also a lost girl looking for a home for herself, someone who tries to integrate into whatever culture she encounters in order, in some ways, to develop a sense of belonging. She has a strong sense of right and wrong, and has rather ruthless ambitions, but she isn't storming into foreign cities to make them more like herself and the culture that she knows. She is still searching for her home and for her birthright, and although she makes many mistakes, and develops something of a superiority complex along the way, she doesn't have an attitude of "freeing the savages," and she doesn't get a free pass for even her well-intentioned behavior. If her story is one of the "white savior," it doesn't paint it in a particularly positive light.