I wouldn’t say don’t post personal information at all. But rather don’t post information that you’re not comfortable with everyone knowing, while being identified and never being able to delete it.
IMO it’s best to assume that if you post enough online, someone dedicated enough will be able to identify you, especially people who already know you in real life. It’s difficult to post without revealing small details about yourself that can be combined to piece together who you are. Eg, you might never say where you work, but your city, field, an offhand comment about a coworker, a mention of a conference, and such might let someone narrow it down. Similarly, you might never mention what city you’re in, but it might be narrowed down from mentions of things like traffic, weather, events near you, remarks of things being close by, etc. And that’s not even getting into devious things like trying to trick someone into clicking a link to a domain you control so that you can get their IP.
I’m of the opinion you should generally act as if you’re talking to people face to face with a name tag saying your full name and address. I think that approach also just plain makes the internet a better place. Anonymity seems to make a lot of people more comfortable being aggressive assholes.
I say “generally” because there’s plenty of valid reasons to want to post things you would want to post things that you’d never say if identified. But in that case, you should strongly consider using an absolutely minimal throwaway account, while being extremely careful with details. And even then, you should at least consider that you might still get identified. In particular, I think a lot of users of throwaways only consider strangers not being able to identify them. Sometimes that’s all you care about, but your family, friends, and coworkers are going to have a lot easier time identifying you.