When Tiana came out there were media reports that said that African American girls were realizing for the first time that they too could be princesses and identify with the Disney princess line. Do you think those girls were being told by their parents, "nope, you can't be a princess because of your ethnicity?" Likelier those girls were told over and over again "you can be ANYTHING you want to be," and they didn't believe it because they didn't see proof: there weren't any African-American princesses up there in the Disney pantheon.
Parents have the greatest responsibility but unless you want to keep your kid in a vacuum, homeschool them and never let them leave the house, interact with other people and get exposed to any sort of media they are going to be influenced, be it subliminally or overtly, by what they see. How well they can stand it depends on how well you've taught them - but on the other hand when they are constantly bombarded with negative images those will stick with them.
How do you think brainwashing works? They repeat the same things over and over again. Why does propaganda work? For the same reason, and it reels in intelligent, critical thinkers.
We learn to normalize what we see every day. We learn to identify what we don't see often as being outside of the norm and, perhaps, inferior. One of the reasons there's been a push to include people with disabilities in media, toys, books, etc. is so non-disabled will see them as normal and not think of them as people to fear, hate, or see as being abnormal. Ditto with non-traditional families, the LGBT community, different ethnicity and religions, etc.
And the princesses are targeted to a very specific and very impressionable age group; they're used as teaching tools and they are held up with role models. There's a reason that responsible children's media groups, like Sesame Street, have psychologists on staff: children have a way of processing and rationalizing things that is very different from adults. The responsibility when you are dealing with children's media vs. adults is greater.
One bit of that McDonald's comparison that does work: if your kid eats Big Macs every day and learns that they are the proper food, they will have issues. If your kid learns to eat healthy and has a Big Mac every once in a while as a special treat, it's not going to kill them. Moderation is important.
Likewise, with the Princess line: If your kid thinks that every single princess or attractive woman has to look a specific way or fit a specific mold, she will have problems. If your kid learns to appreciate different types of beauty and diversity, and can appreciate the sparkly pageant queens and the Meridas of the world as both being special, she will do a lot better. Especially if she grows up to look more like Merida than Barbie.
And this is where Disney has failed - they are supporting the former and not the latter.