People can believe whatever they want. And Ayn Rand is a significant, if rather isolated, person in the intellectual history of the 20th century. Many people have read her best known novels. But by almost any definition she held numerous beliefs, really most of her beliefs, which in ordinary political discourse would be considered far outside the mainstream, extreme and in many cases simply bizarre. In any other political context the person you embrace as your favored philosopher or even the person who you're a follower of ... that person's views are totally newsworthy. Totally ripe for scrutiny. If President Obama repeatedly and openly said he was a follower of Richard Dawkins, no one would pretend that it was somehow off-limits for his opponents to dig into Dawkins' beliefs.
Why shouldn't this apply to Rand Paul? It really does amount to special pleading. He gets to play by a political rulebook that applies to no one else in the country.
Late Update: TPM Reader MB wrote in the following. And I thought I'd append my answer because I think it's a good question ...
I'm no fan of Rand Paul, and far less a fan of Ayn Rand, but this seems to be putting too fine a point on it.
While approximately 99% of what Ayn Rand ever wrote was solipsistic nonsense, she did write an awful lot, not all of it related to altruism and Christianity. To say that it's inconsistent to be a fan of Rand's and be Christian is about like saying it's inconsistent to be a fan of Richard Dawkins and be a Christian. (I'm a tremendous fan of his writing on evolutionary biology, but think his moral philosophy is blinkered. I'm also an observant Presbyterian.)
A reasonable question for him would be, it seems, "Ayn Rand decried altruism and was a stout atheist. Could you explain more of how you reconcile Christianity and Objectivism?" The fact that I think the two are incompatible (largely because Objectivism is a bunch of hooey that appeals to small minds regardless of faith) does not mean that a reasonable person might find inspiration from both.
And here's my response ...
I agree that it's not impossible. And your Dawkins/Christianity point is an apt one. But as you note, it's his core work as an evolutionary biologist you take to rather than his amateur endeavors as an advocate of atheism. It would hardly make any sense that you could be a Christian in conventional terms and also be a fan of his atheism advocacy. So yes, it's certainly conceivable he could be both. But both her atheism and her worship, for lack of a better word, of power is profoundly anti-Christian. So while it's definitely possible one could be both I think it would be well within the realm of reasonable to ask how he reconciled the two. And in the cartoonish and crass realm of 30 second TV ads, that's what was behind Conway's ad.