A lot of right-wingers are very curious about Liberal Conspiracy. All our favourite lefties and many of our favourite ideological curiosities are there.
I think the contradiction that will make it difficult to maintain is that some (I'm thinking Chris Dillow and Gracchi in particular) think "left-liberal" means a libertarian who isn't particularly content with some of the right-libertarian movement's underlying philosophy. Others clearly mean it to be more like an American liberaltarian: Basically a classic statist left-winger with a particular concern for civil liberties. Neither position is illegitimate but they lead to very different practical politics. The ultra-Hayekian viewpoint Dillow advocates, for example, would imply a very small state which is a project a liberaltarian will, at best, spend their time poking holes in.
Now, while I have to write up a long Coasean post and finally tangle with Chris on the economic efficiency of firms (and write more about Rawls) the only real policy difference I can see between him and the very right-wing is immigration. Even there you'll find plenty of pro-immigration libertarians - far more than anti-statist lefties I think. Over at Liberal Conspiracy, by contrast, writers are already writing that "why social and environmental justice are worth spending a lot of society’s money on" is self-evident which suggests statism is likely to rear its head sooner rather than later.
There are important reasons why libertarians and conservatives tend to find themselves in alliance. I detailed them in an article for TCS that I'm still very proud of.
Still, disagreement and controversy on a group blog isn't necessarily a problem. That's generally what drives the Corner's most interesting moments.
I'm not sure what interaction Liberal Conspiracy wants with right-wingers. At first I thought it must want to be a showcase for the best talent the left-wing blogosphere has to offer. Sort of like Comment is Free was originally intended to be. That intention is suggested by the ConservativeHome-like online magazine format and the fact that it has clearly been "marketed" pretty widely. If that is the intention then it could become a great place to go and find all my favourite left-wing bloggers to debate with. The site would want to attract right-wing comment so that the new ideas it purports to promote can be battle-hardened before heading out into the real world.
Unfortunately, one of its very first posts manages a combination of superficiality and self-righteousness that has utterly put me off the whole project. Apparently what Zohra really wants is to escape the real world with all those unpleasant and self-evidently wrong people who disagree - who she never discusses in any tone but utter disdainful incomprehension. She might get what she wants. Ideas and arguments there aren't going to get scrutiny from the Right if we have to wade through such empty-headed sanctimony to get to them.
I've nothing against a forum to discuss ideas among the like-minded. Sometimes you do want to get off arguments about principles. I doubt you'll get that from Liberal Conspiracy though. The Hayekian left is too different to the politics of "social and environmental justice". Also, I'd suggest that if you look at the output of Demos, the IPPR and the other left-wing think tanks and compare it to an organisation like the TaxPayers' Alliance the left needs to do less talking to itself not more - the editor of Prospect expressed the same opinion at their Think Tank Awards this year. Of course that will require Zohra to get over his/herself.
Update: So far the two substantive posts are why we should force students to stay at school longer and why we should ban smoking in public places. It appears the site is less a liberal conspiracy and more a conspiracy to steal the word liberal from its rightful owners.