You can if you're small.
My spouse is going through a similar issue. He is writing a 5 year arc (issue 2 of 20 just came out!) of his own creation, a 17+ (eq to NC-17) superhero comic book with some scenes just a hair's breath short of porn. This series has its own website (with a domain name), Twitter, Facebook, and Instagram. But he does everything under his full legal name.
He has a personal Facebook account which is just for friends and family and a personal Twitter which is public. He talks about all his projects in both.
He's also almost done with a second large comic project, a stand-alone graphic novel aimed at the young adult market. Once that picks up a publisher, he and I will go through and make social media for it too. As for a website, not sure yet. Either it will have its own or we'll make a general one that can have all the "family friendly" work on it together (he also publishes in various anthologies). Yeah, we'll keep the first series separate, with a link to it from a main website.
You can if you're in a niche market.
All of my spouse's work is in comics (or occasional things in comic crossover publications like a mixed anthology). That's a pretty forgiving market when it comes to appealing to a wide range of people.
Paige Braddock does this as well. She is famous for the comic series Jane's World, a strip labeled "too risque for mainstream papers" at the start of its 20-year run. It's a bit different as her strip eventually did hit the mainstream and was never particularly "adult" (it was just lavender). Her new work is Stinky Cecil, a comic series aimed at elementary school children.
Sometimes you can if you're well-known.
Judy Blume lists all her books, from elementary school level to pretty risque adult, all together on her website.
So what about social media?
You're talking more about things like using the same Twitter account for everything. And I think that's a mistake.
Why would you use the same account when Twitter (and Facebook and Instagram) are free? It's a bit of a pain but not hard to switch from one to the other. Another advantage is that people that only want to follow one of your projects (or one set of related ones) can do that without clutter. You can still so some cross posting to encourage followers to check out your other work.
Websites range from free to cheap and I see no reason to combine two very different communities into one, unless you're very tiny. I mean I have a blog with genealogy and recipes and travel info as my main focuses but it's mostly for friends and family so I don't bother to separate the streams (the issue here isn't appropriateness but boredom).
I don't see a problem with putting the occasional "check out my adult works" link on your PG-rated sites or "got kids? they might like my ___ site" links on your adult ones.
Exceptions?
Hardcore porn.
If you're a teacher or another profession where you need to hide what you're doing.
Anything else where crossing the streams could be dangerous or lead to trouble.