If you're finding this question because you're using SSMS and getting this error even though are 100% not selecting Windows Authentication then I can assure you that you're not losing your mind.
On a new Windows + SSMS install I just tried connecting via:
File > Connect Object ExplorerI got the error message about Windows Authentication not being supported (I'm not even using a domain). After trying three times (with SQL Server Authentication selected), I switched to logging in using
Object Explorer > Connect > Database Engineand it worked first time.