I once had a SW interview with a job that had a 2-hour long personality test. No tech questions. Just random questions to test my personality. It started out simple, like 'what was the last book you read' to more in-depth situations that had nothing to do with the job. The manager interviewing me (who admit he basically just started managing a month prior) told me he just read a 'great book on management' and wanted…
I chose the startup, and it has been the best job decision I've ever made.
Personality tests can disclose a lot of personal information. It's unclear where this data might end up or who might have access to it. I detest this practice and consider it a major red flag.
(edit: typos)