Since I have a family, I wonder what a "family show" is ... for my daughters, 8 and 10, "The Simpsons" is a family show. It doesn't mean it has no content kids won't understand. The Simpsons has plenty of content kids don't get. But obviously, there are enough jokes for kids, and relatable characters, in it, too.
I think standards have changed, since when it was new, The Simpsons was considered a very daring and edgy adult sitcom, generating controversy with a lot of its subject matter. But it's become such an indelible part of the TV landscape that its style of humor has become normalized and even seen as tame.
Not unlike how Star Trek was considered a racy, boundary-pushing adult drama in the '60s but became popular with kids in daytime syndication in the '70s and ended up being seen as a family show. It seems to be a recurring pattern that when the standards are loosened for what's acceptable on broadcast TV for adults, society eventually gets so used to it that it no longer objects to letting kids watch it.