False positive and false negative rates also have a relation to the injustice of a false positive. Having to provide ID and get frisked sucks but being falsely accused of a crime and having your entirely life destroyed even if rare is a massive injustice. This is the entire premise of Blackstone's Ratio
https://en.wikipedia.org/wiki/Blackstone%27s_ratio
For what it's worth I'm libertarian and lean towards having false positives for any of those three scenarios.