Growing up my parents didn't really closely monitor what we watched. My mother didn't allow me to watch soap operas as a young child if I happened to be home from school or on summer break during the day, as she thought they were trashy and didn't really watch them herself. Aside from that, I don't recall any TV shows being off limits and when we got our first VCR, a few of my siblings were older than me, and we were able to watch most anything we wanted to rent, even things like comedies that happened to include some risque scenes or double entendres (which were tame back then vs. modern standards). What most "overprotective" parents don't realize is that most of the adult-themed stuff flies past the kids without them realizing what it's even about in most cases and the kids don't even catch on...Unless the parents make a big deal about it or start calling it out and that's when they perk up and start taking notice. There were several movies I watched as a kid that I re-watched as an adult and only then did I actually understand some of the humor or get some of the true meanings.
I also think maybe it's better if kids see some TV shows that deal with more adult themes when they're with their parents, because if they don't understand some of the terminology or something that's said, at least they can ask their parents and get an understanding from them instead of maybe asking older kids at school who may fill them with BS, or look it up on the Web and get a different meaning altogether.
