I wouldn't push it that far, particularly for the John Carter novels. John Carter may be a brave and masterful swordsman, but he wins over his enemies and respect of his allies by treating them fairly and with respect. He wins over the Green Martians by treating them with respect and compassion. He wins over some of the Black Martians by, once again, treating them fairly and with respect. The only Martian race depicted uniformly negatively are the White Martians, who are either deceitful cowardly plotters, or a Wacky Wayside Tribe used by Burroughs to mock philosophical concepts he disagrees with*. (We never see enough of the Yellow Martians to get an opinion.)
Indeed, the books have a very strong undercurrent of racial and cultural tolerance - not mighty whitey in the desert. One of the lines from the second books sticks out "Though we were of three different races, and of two different worlds, none would have thought of abandoning the other." All the heroic characters are ones who overcome their cruelty, bigotry, and intolerance.
(Even the female characters tend to come out well. Sure, Dejah Thorris, the 'Princess of Mars' spends most her time captured, but she is also depicted as a passionate and charismatic speaker and a brilliant scientist. Later books feature Carter's daughters, Tara and Llana, who are depicted as brave and skills swordswomen.)
The books are hardly progressive by modern standards, but hold up far better than a lot of early pulp novels.