Are you "allowed" to print information about other people. Well, the answer to that is yes. Biographies do it all the time. Newspapers include info about people, their families, their ages, their address, the crimes they commit ... everything.
And technically, there is no real difference between "online" and "print". The boundary between the two is blurring fast. Books go online. Online info gets printed.
So no, it doesn't apply less to formal print than it does online.
Whether you should or not is what you're really asking.
You've got to be careful. What's offensive to one person is not offensive to another.
A few ideas about this:
Many years ago, before I knew better, I passed on a genealogy done by my cousin on his side of the family to someone else. When that person contacted my cousin, my cousin was extremely angry with me because he never meant the information to go outside the family.
At family reunions, when people see the family tree that you've given them in that binder, you must ensure that any family secrets or whisperings are not included. The divorces, illegitimate children, adoptions, etc. that people don't want to know about. It's not so much a legal thing. It's a human thing.
In the book that Aunt Mabel writes, she's entitled to write whatever she wants. For that matter, it doesn't even need to be true and only is what she believes to be true or could be fiction she made up. If it is slanderous, she could be sued. But if she's the sort that doesn't care and wants these stories to be told, they'll be told. Look at all those shocking biographies or autobiographies that are out there. These include stuff that's way worse than you're thinking about and implicate others, not just the writer.
You'll have to decide what level you're willing to go. But there is no correct level. No matter what you pick, some people will tell you you've gone to far, and others will say you haven't gone far enough.
Just be careful and don't include the family secrets that people don't want divulged.