A Princess of Mars was both written and set in times of distinct change. The story shows this sense of transformation through dichotomies without definite answers. The structure itself also forms a transition point, beginning with the epistolary style of the 19th Century and the Gothic horror scene in the cave, leading into the modern Scientific-based fiction of the main story. In particular, Burroughs' descriptions of races is transitional, and needs more interpretation than a simple labelling.
On Earth, Carter doesn't show the stereotypical view that all 'Indians' are bad, mentioning having spent time living with the Sioux. However he shows a fear, potentially justified, of the Apache warriors which is in keeping with the time the story is set.
When Carter describes his Green Martian captors as 'savages', it is a technically accurate description as they are indeed 'fierce and violent'. Yet he also acknowledges that other attitudes exist within the Thark. Burroughs' tentative dealing with the communal natures of Thark society was in part due to the contradictory prevailing political attitudes towards events in the Russian Empire at the time he was writing. This is also shown in his portrayal of women, who are both powerful and powerless in all societies on Barsoom.
The Red Martians are portrayed as the "good" race and are set up oppositionally to the Thark, being imperial not communal, 'civilised' rather than 'savage'. Yet it is also made clear that neither are mammalian like humans. This could be interpreted a way of showing that humanity isn't limited to and one race or species, but is instead something that is demonstrated in characters possessing an attitude of tolerance, compassion or caring. Although still viewing the Barsoom races as wholes, he remains able to see them also as individuals when not indirect combat with them.
Thus it can be said that A Princess of Mars is a story written in transition from the Victorian to the Modern world, which itself marks a change from the Gothic novel into Science Fiction.
Dictionary.com definition of Savage
Edgar Rice Burroughs' Martian novels as an early paradigm of racial toleration by Ronnie W. Faulkner
A Princess of Mars / Edgar Rice Burroughs [etext from Project Guttenberg]
Edited and updated essay:
To be added later