It's quite safe. As other answers correctly stated, yes, it may contain some bits of information about your machine and server process (depending on where the id was generated, in meteor or mongodb server)
But to leverage them for any malicious actions is a tough task. An attacker pretty much needs to get inside your network to do anything. And if he's in your network, you're screwed anyway, regardless of what ID format you expose.
By any measure, ObjectId is more resilient to guesses than a regular auto-incrementing integer ids you find in other databases. And they're exposed all the time!
Note, though, that you shouldn't rely on the fact that an id is hard to guess. Protect private pages with authorization checks, etc. So that even if an attacker correctly guesses an id of a page he shouldn't have access to, he is refused the access.