It’s all one ideological package. From historical documentation, such as writings and interviews of those in her inner circle, we learn that she was fanatically insistent that everyone accept every aspect of her philosophy, even her odd aesthetic views (which some see as eerily similar to Soviet Realism.)
Even if one of the main ideas of an author seems OK, this does not mean that the author should be read. She is clearly trying to indoctrinate people into a very specific rationalist, secularist worldview. I would no more want my kids reading this, than reading Xian apologetics, Chairman Mao or L. Ron Hubbard.
Although I don’t agree with them, it’s understandable that many people believe that private charity should take care of all poor people, with government doing very little or nothing in the chesed department.
However, Rand’s extreme libertarian or anarcho-capitalist views are also incompatible with the Torah’s economic laws, such as the requirement to pay a worker on the same day as he finishes his work. Any legislation of that nature would be absolutely forbidden under Rand’s worldview, as presented in the interview you quoted. Similarly, Poskim have approved of tax collecting, which is also against Rand’s beliefs.