A chatter post inherits its sharing access from the parent entity.
If OWD is private for an object, then users that the object is shared to can view the record or post.
If the records are shared through Sharing rules or manual sharing, then the users can view the feeds on the records.
So, if an user have access to the record, then the user can view all the chatter feeds related to that record.
Follow people and records to see updates about them in Chatter feeds on profiles, groups, the Chatter tab, topic detail pages, and on record detail pages.