I like to think I'm CC w/ a hefty dose of cultural relevance thrown in. I think CC ties in w/ the unschooling mentality as well.
One thing that I can really see a difference in is dealing w/ the play area at the mall. I sit on the bench, read a book or chat, and periodically glance up at DD. If she's out of sight I might stand up and locate her. If she gets upset/frustrated, falls and is upset by it (sometimes she is either because it hurt or made her mad, and sometimes she isn't) or has a negative run-in w/ another child and cries, I intercede and comfort her. If she starts messing w/ peoples' stuff, poking a baby, or exiting the play area, I grab her and relocate/redirect her. But otherwise I sit there and let her play.
Other people I see in the play area react quite differently. They follow their crawlers (and even toddling walkers) around, staying w/in a foot or two. They help them up on things, over things...they won't let them figure ANYTHING out for themselves. I sometimes show DD a way to do something she can't figure out that's frustrating her, but often as not she finds some different way to do it on her own anyway. I do watch her quite a bit, but because I find it entertaining and I'm in the mood to do so. Periodically she'll look over at me to catch my eye and we smile at each other, but she'll go out of site in the play equipment (in the open sided box shape or the crawl-thru or some such) for minutes at a time, busy interacting w/ the other kids and paying me no nevermind.
At home I can't walk in the next room w/out her fussing. She thrives on interaction w/ other children, especially older ones. So I seek out situations where that happens. I'm starting back to school soon, and she'll be cared for in a home care situation w/ other kids of varying preschool ages. It's a situation I think she'll fare much better in than she would w/ just a solo provider. She doesn't even tolerate being left alone w/ DH for long, but if other kids are around she does fine.
I see AP as being about meeting childrens' needs rather than making them secondary to adult needs. I see CC as making this fit in w/ meeting adult needs as well. I'm going to include her in my life, but not give up on my life.
My obsession w/ homeschooling, cloth diapers, etc. vastly predates actually having a child, so I can't really blame it on DD. Actually having her has alleviated it all somewhat!
And I enjoy playing w/ DD and reading to her, but only do these things when I'm in the mood to do so. If I'm doing dishes or cooking, she may get into the tupperware cupboard, stand at the edge of the dishwasher and watch, sit in her highchair playing w/ a cup or spoon, or be on my back or hip if that's where she really wants/needs to be.
DH is a lot more "keep her out of stuff" minded. I go along w/ it as much as I do only because I don't want to clean up the aftermath of, for example, DD pulling half the DVD's off the rack, not because I particularly don't want her into them (she can't open the cases yet so won't damage them and they certainly aren't going to hurt her). I let her get into the utility drawer w/ the hammer in it, I just moved the nails to a drawer out of her reach. I could go on. We don't gate the stairs, but I admit I do sit at the foot of them while she's exploring them. Maybe I should back off...