Ches defined the Collaborationist Catholic far better than I could have done, but as he went for it at the individual level, I'd like to suggest how it works at the national level.
At least one Bishop made a bit of a name for himself within the Circle when he said he was one who spoke truth to Power: he articulated what much of the Bishops' Conference and its staff, and the diocesan staffs, have been about for ages, but missed out the fact of the complete self-delusion that accompanied the self-image. (His, if not he, were a bit slow to admit that it was a quote and not his own bon mot, as well.)
Anybody who heard somebody involved in Catholic education saying that s/he had "been talking to Andrew Adonis" either bought into the fact that here was someone who had dealt with Lord Adonis, when he was Parliamentary Under Secretary at the Department for Children, Schools and Families, and had talked truth to Power; or, and in my opinion, more likely, saw someone who was so sucked into the fact that s/he was talking to almost a Minister that s/he would gladly negotiate away the Catholicity implicit in whatever proposition being debated at the time, just to be able to say that s/he had communed with those at the centre.
The truth is that the Catholic Church in England and Wales was turned inside out by Tony Blair: we got absolutely nothing in return for embarrassingly unctuous fawning. Even worse: now Blair and his party have been stripped of all power, the usual suspects are still spouting the same rubbish that was rubbish even when Power pretended to listen when the rubbish masqueraded as Truth, but to exactly the same people. We're being patronised by the Opposition; the Government is simply ignoring us.
The line is always the same: you have to be at the centre to influence what's going on; you won't get everything, but you can safeguard your core interests. You can't, of course, because you're dealing with people who are much better than you are at this sort of thing, and who aren't going to compromise the way that you are, because they aren't amateurs like you are. The end result is that you end up with nothing except "access", if you're lucky, and nothing except "access" for your new agents who are ideologically compromised with their interlocutors, if you're unlucky. We're really, really, unlucky.
One thing about the current Cruddas/OP issue is odd, though: this is an internal-to-the-Magic-Circle issue which seems somehow to have leaked out, and which has grown legs. This isn't because of the five or six bloggers involved: I don't think we count for that much in the Catholic blogosphere in E&W, never mind further beyond ("Ringo isn't even the best drummer in the Beatles"). How has it gathered such traction?