My mum taught me to read really early on (just after I was 3) so I was always very advanced when it came to books. I found that books aimed at my age group just didn't hold my interest, so I moved on to books intended for older kids.
I remember being told off in school in year 4 because I brought a Jeffery Deaver novel to school (for those who haven't read them, they're fairly gruesome crime novels- the ones I read were about a quadriplegic detective named Lincoln Rhyme). My teacher thought it was really inappropriate for me to be reading it aged 8. She called a meeting with my mum to discuss this and my mum pretty much told her that I can read what I like. It never affected me in any way. If anything it was less scary to me at the time than an episode of CSI yet everyone was allowed to watch that (I didn't really watch a lot of TV, I preferred to read). Eventually the whole thing was dropped and my teacher didn't say a word when I showed up a while later with much darker themed novels. I kept trying to push the boundaries by finding the most depraved and gritty crime novels I could and reading them in school.
I got told off again by my form tutor in year seven for reading the scarlet letter in form time 'silent reading'. I think it was less to do with me reading the book than it was about her disagreeing with its themes and the fact I was reading a book about adultery in a room full of impressionable kids? I don't know. Either way, my mum said pretty much the same thing: that she trusts me to decide what I read.
So to actually answer the question: no. I wasn't banned from reading certain books. My parents trusted me to read books I liked rather than things they decided I should read. Proper children's books never really held my interest, so I moved onto books intended for older teens and adults in about year 3 or 4. I did still read some books for children (like a series of unfortunate events and CHERUB etc.) but my parents never stopped me if I wanted to buy books from the adult section.