Conditional Formatting in a Matrix with Multiple Levels

Does the below work for you? I think the piece you are missing is that you do want to still filter by years, which you can accomplish by adding VALUES( Date[Year] ) as a filter argument of CALCULATE. The ALLSELECTED was making it so all filters from Date were getting removed. E.g.

MaxInRowContMargin = 
VAR __MaxUnits =
CALCULATE( 
    MAXX( SUMMARIZE( 'Date', 'Date'[Year], 'Date'[Month] ), [ContMargin] ),
    REMOVEFILTERS( 'Date' ), VALUES( 'Date'[Year] ) 
)
RETURN
IF(
    [ContMargin] = __MaxUnits,
    "Light Blue"
)

Note that I summarized Date by Year and Month columns, but I believe the above should work with your VALUES( [Month Year] ) instead of a summarize, too.