Thirty years ago, a lot of US states thought it would be a good idea to compute someone’s drivers license number (DLN) from their personal information . In 1991, fifteen states simply used your Social Security Number as your DLN. Eleven other states computed DLNs by applying a hash function to personal information such as name, birth date, and sex. A few other states based DLNs in part but not entirely on personal information.
Presumably things have changed a lot since then. If you know of any states that still do this, please let me know in the comments. Even if states have stopped computing DLNs from personal data, I’m sure many organizations still compute IDs this way.
The article I stumbled on from 1991 gave no hint perhaps encoding personal information into an ID number could be a problem. And at the time it wasn’t as much of a problem as it would be now.
Why is it a problem if IDs are computed from personal data? People don’t realize what information they’re giving away. Maybe they would be willing to give someone their personal information, but not their DLN, or vice versa, not realizing that the two are equivalent. They also don’t realize what information about them someone may already have; a little bit more info may be all an attacker needs. And they don’t realize the potential consequences of their loss of privacy.
In some cases the hashing functions were complicated, but not too complicated to carry out by hand. And even if states were applying a cryptographic hash function, which they certainly were not, this would still be a problem for reasons explained here. If you have a database of personal information, say from voter registration records, you could compute the hash value of everyone in the state, or at least a large enough portion that you stand a good chance of being able to reverse a hashed value.
 Joseph A. Gallian. Assigning Driver’s License Numbers. Mathematics Magazine, Vol. 64, No. 1 (Feb., 1991), pp. 13-22.