I always had a problem with this (very American, in my view) concept of "appropriate". What does it mean exactly? It seems to be hiding stuff that is either ill-defined or unlikely to withstand deep scrutiny.
I have no problem believing that depictions of sex and violence might be bad for young children in some way, but I would argue that there is a burden on people who claim this to spell out out the bad consequences could be.
Is it that it affects children psychologically? If that is the claim, in what way? And is there any research that shows this to be the case?
Or is it that they could say something that would create social embarrassment for the parents? If that is the case, one has to ask: does it make sense to place such a burden on free culture for this rather minor reason? And doesn't it just perpetuate useless social norms?
In the end, I suspect this is (at least partially) good old-fashioned puritanism. I am willing to accept that I am wrong, but I think I am right in reacting with scepticism towards vague moral proclamations such as "it is inappropriate!"