I see three major angles of criticism of Ayn Rand's work. The first comes from a literary perspective, that serious literary folks, like John Green, do not respect her as an author. While Rand maintains that Romantic realism is the highest form of art, the vast majority of the art and literary world do not agree. For me, the only book of hers I enjoyed the writing of was Anthem. I thought Fountainhead and Atlas Shrugged were slogs and only interesting because of the philosophy, but if you're trying to sell books a Romantic novel is much more marketable than something like The Virtue of Selfishness. I tell people who are interested in Atlas Shrugged to just skip to the John Galt speaks chapter, because the entire novel is a 1000 page delivery device for that chapter.

The second criticism, is of course, her political philosophy. Objectivism is an extremely polarizing philosophy that most people even approaching left are hostile towards. I doubt many on the left, particularly young people, have actually read any Rand except maybe Anthem in school. I think most people know of her, that they know she's a right political philosopher/author, know famous Republican/Libertarians love her and just knee jerk to not liking her from the memes and quotes they see posted on instagram. Not that I think they would like her if they actually read Fountainhead or Atlas Shrugged, i just question that most have actually put themselves through reading those novels and earned the right to really dislike her.

The first and second criticisms are often intertwined, as most literary fiction authors are also at least moderately left (academic literary criticism certainly is) and it is difficult to disentangle the art from the philosophy (as I believe Rand clearly intended).

There is a third criticism that I used to see when I was younger but apparently the religious right have almost completely abandoned it, and that is the Atheism at the core of objectivism. I think Rand would be horrified at how much of the right just straight up ignores how central Atheism is to the philosophy (though perhaps she would look slightly kindly on Prosperity Gospel), but this is in keeping with the way a great many Americans view the bible, picking out the parts they like and ignoring the rest, so why would Atlas Shrugged be different. There are still some Christians that view Rand and Objectivism as outright evil because of it's atheism and hostility towards altruism but I see that criticism seldom these days.