As a good rule of thumb: if you really want the job, do not volunteer potential employers anything about yourself that you don't think would help you get hired. They aren't cops or courts; depending on how laws are crafted state-to-state, they are legally allowed to consider some categories of information that they aren't legally allowed to ask you outright if you volunteer it.
*There are protections in place for the bureaucracy itself, but they were implemented for practical reasons early in the country's history when it was observed that a party change leading to a clean sweep of the federal government right down to the last front-desk agent regardless of their capabilities in the task at hand was highly inefficient.
Agreed on everything else.