I wrote a response in the comments section essentially suggesting that some beliefs are more deserving of mockery than irenic engagement (anti-vax, young-earth creationism, homeopathy, Holocaust denial, etc.), and that it's not anyone's job to treat any given beliefs with deference by default; rather, it's the job of those who believe to show that their beliefs are worthy of respect by engaging in rational discourse.
After reflecting on my comment though, I think I could take an even stronger stance: the very idea that beliefs need to be respected is fundamentally misguided. It's true that beliefs are, as Randal says, an "extension" of the person—their experiences, biases, values, etc.—but beliefs need not define a person. Moreover, beliefs don't have feelings. They can't suffer indignity. They're just ideas, and ideas can be and often are ridiculous, absurd, false, or cruel. And frankly I have no idea what it even means to say that I "respect" a belief that I think is ridiculous, absurd, false, or cruel.
I don't need you to respect my atheism
I really could not care less whether anyone respects my rejection of theistic claims. If someone chooses to mock my beliefs, I'm not going to lose any sleep over it—chances are they've just completely misrepresented my beliefs anyway, like the meme which claims that atheists believe "nothing magically exploded for no reason". It's intended to be mockery, but it bears no resemblance to what any atheist actually believes, so why should I or any other non-believer be upset about it?
I think this idea that beliefs are things that need to be treated with deference is a marker of insecurity. Why should anyone's beliefs be exempt from satire, mockery, commentary, and criticism simply because it is an "extension" of their personhood? People's beliefs can and do change. No matter how much conviction someone holds in their beliefs, the right argument or evidence can be persuasive. Does a shift in belief on one topic mean that the person has fundamentally changed? That their attitudes, values, and outlooks are now completely usurped by a new paradigm? Unlikely. More likely is a modest shift in perspective related to that particular issue.
What I do care about is that, if someone wants to change my mind about atheism, they show me the respect of representing my beliefs accurately and engaging my questions and commentary in a substantive, irenic manner. Now, if someone doesn't particularly care about changing my mind and would just rather poke fun at my beliefs (or what they think I believe), that's perfectly fine; after all, there are plenty of times when I'm not concerned with changing anyone's mind myself. And hell, sometimes even irenic dialogue is just as much for the exercise of it all. I don't think anyone who debates with William Lane Craig or Richard Dawkins would expect them to change their minds, and that goes for those all the way down to anonymous Disqus commentators.
Taking theism down a notch
A central theme in The God Delusion is that openly criticizing religious beliefs has long been considered taboo. We're expected to show deference to others' beliefs, even if we find them absurd or dangerous. Dawkins, along with the rest of the new atheists, deserve credit for helping to erode that taboo, moving religion toward the same marketplace of ideas in which everything else we believe is discussed, disputed, challenged, mocked, and satirized.
I'm a huge fan of the essay No, you're not entitled to your opinion by Patrick Stokes. He says,
If “Everyone’s entitled to their opinion” just means no-one has the right to stop people thinking and saying whatever they want, then the statement is true, but fairly trivial. No one can stop you saying that vaccines cause autism, no matter how many times that claim has been disproven.
But if ‘entitled to an opinion’ means ‘entitled to have your views treated as serious candidates for the truth’ then it’s pretty clearly false. And this too is a distinction that tends to get blurred.
You are not entitled to your opinion. You are, as Stokes eloquently observes, entitled to what you can argue for. I certainly respect theists' civil and human right to believe whatever they wish. But if they wish to influence others with said beliefs, then those who do not share them have every right to rigorously challenge them—and that includes ridicule, satire, and mockery. If you're not ready to see your religious beliefs treated the same way our society treats every other idea—contentious, controversial, fair game for all manner of discourse and even derision—perhaps you don't really have as much conviction in the strength of your beliefs as you'd like to tell yourself you do.