OK, just to add my tuppence worth to a really interesting but probably-should-be-dying-by-now thread.....
I am the 'lax' parent of which OP, LeQueen and others speak. Sort of. I don't accept my DCs trashing property, being violent, rude, etc. I'm pretty sure we're all in broad agreement about the kind of attributes we like in other adults and therefore are finding the best ways we can to try to nurture these qualities in our DCs.
However, I don't like to parent too publicly if I can avoid it. I try to avoid taking a tone with them that I'd object to someone else using with me, and I don't want to risk 'shaming' my DCs and feel our relationship is put under too much strain by having others bear witness to our more difficult exchanges. I will intercept offending behaviour by any means necessary (firstly by telling them it's not on, then ultimately going home from someone else's house, leaving a restaurant, etc.) but I will try to do so in a calm, kindly manner. And will try to talk it through with them once the heat of the moment has died down. Probably have been known to say 'don't do that, darling' in a wimpy voice on more than one occasion
My DCs are by no means perfect, probably have caused more than their fair share of cats bum/lemon sucking faces out and about, but I genuinely believe I'm doing the best I can given the sort of person I am, the ideas I hold, the way I want to relate to them. And somehow have managed to hold onto some very dear friends who are much more of the LeQueen ilk. They're doing time-outs with a kitchen timer in one room, I'm having a toddlers conciousness-raising workshop in another [grin} I think we all just accept our differences and respect them enough to work around them.
But what irks me and what so many people seem to get wrong is that just because I'm a 'soft' parent this doesn't mean I haven't thought it through. Just because I'm not parenting in the way that you do or in a way that's immediately to apparent to onlookers, I am still parenting. Actively. Like others have said, I hate the assumption that anyone who doesn't do things in the same way must be lazy or inept.
I was amongst a group of older (as in had DCs twenty odd years ago) women today and they were commenting on the outrageous behaviour of the children in some tv documentary. They were like a puffed up Greek chorus of lemon sucking: children have too much control these days, in my day we'd have given them a slap, children just need to be told what's what... etc. I'm troubled by how this school of parenting feels that it's got the monopoly on conscientiousness.
Like I said, we all want the same things ultimately. Let's just respect each others choices, concentrate on our developing relationships with our DCs, and fit friends in around that. Either with or without DCs, whichever's most harmonious.