There's no gore or anything like that, unless you dig VERY deep into some of the boards. /b/ is full of porn. so... yeah. Nothing horrifying, ever. /r9k/ and [s4s] are the good boards. The humor on the site has not been dark for many years, and if you hear bad things about them, it's outdated. Even /pol/ is no longer that alt-right board you have heard of. tl;dr: Only stay away if you are not allowed to see pornographic content. Trust me, gore appears very rarely, I visit /b/ many times, and no.... there is no gory stuff.
4chan is a fully anonymous imageboard/forum site with boards dedicated to varying forms of content and discussion. There are many boards on this site, too many to list here, all with varying degrees of child safety. Some boards such as /h/, /gif/, /aco/, /r/ and /s/ are dedicated to pornography, while others such as /pol/ and /b/ are notorious for their offensive content. However, there are many boards which are perfectly safe for older teenagers such as /wsg/ (worksafe GIFs), /vr/ (retro games), /lgbt/ (gay community), /news/ (current news), /int/ (international) and /trv/ (travel). These boards can still contain some risque content, but nothing too explicit to be considered "pornography" at all. Overall, very good site for those with a thick skin, but not for kids. No doubts 18+ for NSFW boards and at the very least 15+ for SFW boards.
Dear god don't let your kids on here. This website is safe, a forum for anonymous discussion, but sometimes some really fucked up stuff can appear. It's okay if you can tolerate it, otherwise don't come onto this website.