I am not a fan of Mary. I understand why some people feel she's "fake", "shallow", "arrogant" etc.
Mary is probably the one who changed the most after dating/marrying her prince. She changed her accent, skin (thanks to a well-published skin consultant), style (thanks to a well-published stylist), lost weight etc. in order to look more royal. Sure, other princesses also become more polished with more money. But Mary changed the most. That gave the impression of her being fake. She's no longer the a bit chubby, sporty, tan Australian woman in tank top. She's now a creation all the money can buy.
As for being shallow, this has a lot to do with all the "fashion icon" business. She did much more than just attending several fashion shows "in support of Danish fashion industry". She's actively hyped as a fashion icon by Danish, Australian press and perhaps, Danish court. She modeled foreigners' clothes and posted for fashion magazines. No other princesses in recent memory have ever done that. (Diana did the fashion shoots after her divorce. Plus, if I remember correctly, Diana wore her own clothes for the shoot.) When she acts more like a celebrity than a royal, it's not surprising that a lot of people have the impression of a shallow person. The fact that she was shown as "turing it on" for the camera but no interest in the event she's attending doesn't help.
Mary also has a very haughty body language. The chin-in-the-air is well noted, even by the painter of her portrait. She also extended her hand in this very hauty way that I just found very offputting. She would hold her hand out in a 45 degree angle down from her wrist. It seems to show her superiority or reluctance to shake the other person's hand. She's caught on photos like that often before.
I personally don't think she's arrogant. I do think she's very insecure. A confident person wouldn't have changed so much after marriage. She seems to think the haughty body language is how a princess supposed to be and she wants to be seens as a true princess. It's another new thing she adapts after marriage. She's the most at ease interacting with children because she knew children were star-struch and wouldn't judge her poor Danish or lack of intellectual capacity. I don't think she has much intellectual depth from all the interviews she gave. She's inarticulate even in her native English. But again, since Fred isn't exactly an intellectual giant himself. Mary suits him just fine.
These are just from my observations. I don't mean to offend any Danes or Aussies.