There seems to be a large group that detests her. Where is that coming from? (Honest question looking for facts, not to start a pointless debate).
The reason why is because the vast majority of people I've ever met who bought into her ideology were selfish assholes who used the writings of Rand as a pseudo-intellectual justification for their selfish assholeness.
So in a way the hatred is personal, though a couple of steps removed from Ayn Rand the actual person.
The market, and the self-care that drives it, are wonderful mechanisms, and have brought great wealth. But (stating the obvious) humans need more than being able to buy and sell at will. They need health-care, education, welfare, etc (even if their parents / family happens to be poor). There are other factors than market-fairness that a civilized society should take into account. Not doing so is economism. And almost every one of us probably knows someone who would have been left to rot/die by Rand'ists if they had it their way.
So I would not say it is (just) hate that makes people stop listening when Rand comes up. But rather a kind of (not very laudable) impatience with naivite, that might be familiar to anyone who ever did any teaching, or for example tried to guide a novice elderly person through using a computer.
So far I have failed to find any well-reasoned criticisms -- most of the criticism appears to come from people who misunderstand her work (or perhaps I do). I think the topic is ripe for analysis.
In general, from the standpoint of someone against it, Objectivists seem to think that poor people and welfare programs are preventing the wealthy from "saving the world", totally disregarding the fact that poor people do all of the labor and numerous examples of wealthy people encouraging legislation to prevent competitors and innovation.
[1] - http://michaelprescott.freeservers.com/romancing-the-stone-c...
No matter how much one dislikes an idea, I think one should be willing to understand and engage with it, especially if it's an important idea that has had influence (as some of Rand's ideas have, for example, her concept of "force").
I personally agree with most of Rand's philosophy, but that doesn't prevent me from being willing to listen to and engage in discourse with Marxists, Keynsians, and other schools of thought which differ strongly from Objectivism.
If someone really thinks their ideas are true and right, then they should have the confidence to see those ideas tried and tested in the real world, against all the alternatives.
They should count it as a privilege to discuss/debate their ideas with opposing schools (as long as everyone respects basic manners/decency), because doing so will deepen their knowledge and improve their ability to convince others of their ideas.
Anyway enough ranting. :)
My idea is that dropping a bomb on you would immeasurably improve the world. Care for me to try that, or are you ready to admit that some ideas shouldn't be tested?
A lot of people do dislike her as a semi-famous figure (i.e., not having known her personally) because she has said and done some things that are fairly disagreeable. (The easiest potshot to take is that her ideal human is a sociopath.) But by and large, it's because she's had what is often perceived to be a very negative impact on society.
Here's a biased, first-person, but vitriol-free perspective: http://www.salon.com/2011/04/05/my_father_the_objectivist/