The district she won is a working-class one, and she sold herself as an "everyman" fighting for their interests. What gets lost in the noise is that while she was born there, she spent most of her life growing up and living in an extremely wealthy District not far from there. In terms of actual upbringing, she's much closer to a Romney or wealthy establishment type then she is a Joe plumber.
That's not to say she isn't capable. I'm just simply pointing out that her image as she sells it doesn't match her profile.
Edit: this whole rent thing is actually a great example. She can of course afford an apartment. However, she wants to play up the image of someone struggling to pay their bills, so she pushes this story.
However, I'd like to point out that Trump did the exact same thing, less successfully, and the people criticizing her were once vocal proponents of him, so it comes off as incredibly hypocritical.
That is a completely fair point. The problem comes if you're trying to claim that you're better than him. It's difficult to maintain the high ground when you're using his playbook, and ultimately Cortez would be worse off if the general perception of her was that she was just another Trump.
So yes, people criticizing her that praise Trump for this specific issue are being hypocritical, but only because she is being just as hypocritical over the exact same issue.
Maybe, I'd definitely have to see some evidence for her situation other than that, whereas Trump has been on record bragging about his fortune several times, so it's still a different situation. I was just pointing out the hypocrisy of them saying she did it, and ignoring that Trump blatantly did.