Yep. This can be as small as "Hey there was a crime committed in this town, we need to take all the computers to check for clues" to as large as "We need to know who checked out this book, give us those records" to "Hey we just want to go on a fishing expedition, let us see your records"
This can be contentious. Many (most) libraries have privacy policies that prohibit giving up this information without a warrant. Every state in the US has patron privacy laws at a state level. Here are a few links to look at.
Things that are common IT sense aren't always common sense at small and rural libraries where the librarian may be the only IT staffer. Libraries use software to help them do this, but it's a challenge for many small libraries to keep up. Library associations do the best they can to disseminate best practices for stuff like this.
I'm the one who made the original signs, always great to come and talk radical librarianism with people. Feel free to subscribe to my newsletter.