I think the danger here is far smaller than people are making it out to be. There is a major difference between the label "rationalist" and most other identities as Paul Graham refers to them. The difference is that "rationalist" is a procedural label; most identities are at least partially substantive, using procedural/substantive in the sense that the legal system does.
"Rationalist," which I agree is an inevitable shorthand that emerges when the topic of overcoming bias is discussed frequently, is exclusively a procedural label: such a person is expected to make decisions and seek truth using a certain process. This process includes Bayesian updating of priors based on evidence, etc. However, such a label doesn't commit the rationalist to any particular conclusion ex ante: the rationalist doesn't have to be atheist or theist, or accept any other fact as true and virtually unassailable. He's merely committed to the process of arriving at conclusions.
Other identities are largely substantive. They commit the bearer to certain conclusions about the state of the world. A Christian believes in a god with certain attributes and a certain history of the world. A Communist believes that a certain government system is better than all others. These identities are dangerous: once they commit you to a conclusion, you're unlikely to challenge it with evidence to ensure it is in fact the best one. That's the kind of identity Paul Graham is warning against.
Of course, these labels have procedural components: a Christian would solve a moral dilemma using the Bible; a Communist would solve an economic problem using communist theory. Similarly, rationalism substantively means you've arrived at the conclusion than you're biased and you can't trust your gut or your brain like most people do, but that's the extent of your substantive assumptions.
Since rationalism is a procedural identity rather than a substantive one, I see few of the dangers of using the term "rationalist" freely here.
Some people here have argued that 'rationalist' refers to someone who wants to act rationally, as opposed to someone who actually puts the necessary techniques into practice.
I think the danger is far greater than you suspect.
I've noticed that here on Less Wrong people often identify themselves as rationalists (and this community as a rationalist one -- searching for 'rationalist' on the site returns exactly 1000 hits). I'm a bit concerned that this label may work against our favour.
Paul Graham recently wrote a nice essay Keep Your Identity Small in which he argued that identifying yourself with a label tends to work against reasonable -- rational, you might say -- disscusions about topics that are related to it. The essay is quite short and if you haven't read it I highly reccommend doing so.
If his argument is correct, then identifying with a label like Rationalist may impede your ability to be rational.
My thinking is that once you identify yourself as an X, you have a tendancy to evaluate ideas and courses of action in terms of how similar or different they appear to your prototypical notion of that label - as a shortcut for genuinely thinking about them and instead of evaluating them on their own merits.
Aside from the effect such a label may have on our own thinking, the term 'rationalist' may be bad PR. In the wider world 'rational' tends to be a bit of a dirty word. It has a lot of negative connotations.
Outside communities like this one, presenting yourself a rationalist is likely to get other people off on the wrong foot. In many people's minds, it'd strike you out before you'd even said anything. It's a great way for them to pigeonhole you.
And we should be interested in embracing the wider world and communicating our views to others.
If I was to describe what we're about, I'd probably say something like that we're interested in knowing the truth, and want to avoid deluding ourselves about anything, as much as either of these things are possible. So we're studying how to be less wrong. I'm not sure I'd use any particular label in my description.
Interestingly, those goals I described us in terms of -- wanting truth, wanting to avoid deluding ourselves -- are not really what separates "us" from "them". I think the actual difference is that we are simply more aware of the fact that there are many ways our thinking can be wrong and lead us astray.
Many people really are -- or at least start out -- interested in the truth, but get led astray by flawed thinking because they're not aware that it is flawed. Because flawed thinking begets flawed beliefs, the process can lead people onto systematic paths away from truth seeking. But I don't think even those people set out in the first place to get away from the truth.
The knowledge our community has, of ways that thinking can lead us astray, is an important thing we have to offer, and something that we should try to communicate to others. And I actually think a lot of people would be receptive to it, presented in the right way.