Your syntax is correct (as long as the tables actually have the fields you specified). I replicated the query you have here on my own system and it ran as expected. My assumption, then, is that the issue is with the data. Most likely your data doesn't quite match or you have a duplicate. Let me explain each possibility.
One way your data might not match is if the date fields are storing actual dates that weren't copied from one to the other. Date fields usually store the entire date/time value, which means that two values might be on the same day but won't be equal because they are one second different in time (or less depending on the precision of your date type). You should check to see how the dates are stored. It would be an expensive query, but you might have to parse out just the date portion of each value and compare them (or create a calculated field).
Duplicate rows that match your criteria will also be a problem. If you have two rows that match your criteria then the sub-query will return two or more rows. That isn't ok. SQL will crash. To fix this, you could limit your sub-query to the TOP 1 rows like so:
SET rdc_lb.mrop=(SELECT TOP 1 makeready.mrop FROM makeready WHERE makeready.date=rdc_lb.date and makeready.shift=rdc_lb.shift AND makeready.ns=rdc_lb.ns)
That only works if it is ok to choose only the first row (if the second row would have the same data, for instance). Otherwise, you are going to need to find a different way to figure out which row to choose (maybe order them in descending order based upon creation date and then select the top one so you get the latest value).