There are generally two types of information in applications, "public" and "privileged". The former has the IDs and such discoverable by an index or explore page, the latter requires authentication and has user-specific permissions.
For both cases, if hiding IDs is the only access control on the backend, it's fundamentally flawed. For both cases, if the access control is implemented well (in addition to rate limiting), integer vs UUIDs don't make a difference.
What do you think?