Filter multiple columns with one column

The first thing I would do is create a separate table with a distinct list of colors.

You could do this by creating a calculated table with an expression like the following:

Colors = DISTINCT(UNION(DISTINCT(Table1[column A]),DISTINCT(Table1[column B]), DISTINCT(Table1[column C]),DISTINCT(Table1[column D]) ))

Then I would rename the column in this table from [Column A] to simply [Color] as it's no longer directly linked to ColumnA. I would then use this new column in your slicer.

Then I would create a measure like the following and put a filter on your table visual where this measure is >= 1

Count All 2 = countrows(Filter(Table1
, Table1[column A] in values(Colors[Color])
|| Table1[column B] in values(Colors[Color])
|| Table1[column C] in values(Colors[Color])
|| Table1[column D] in values(Colors[Color])
))

To achieve your matrix result I would put the Colors[Color] column on the rows then create 4 measures to put on the columns which use expressions like the following (creating one measure for each of columns A, B, C and D):

Count A = CALCULATE(countrows(Table1)
, TREATAS(values(Colors[Color]), Table1[column A])
)