GNU date recognizes days of the week and their three-letter abbreviations (plus tues, thur, and thurs), for example:

$ date --date="monday"
Mon Jun 26 12:00:00 AM CEST 2023
$ date --date="mon"
Mon Jun 26 12:00:00 AM CEST 2023
$ date --date="tuesday"
Tue Jun 20 12:00:00 AM CEST 2023
$ date --date="tue"
Tue Jun 20 12:00:00 AM CEST 2023

uutils date, using parse_datetime, doesn't recognize any days of the week and returns an "invalid date" error instead.