Multicolumns filter

Aikeno 

The first thing is creating a new table with distinct values of Contact and Backup.
You can do as follow :

DistinctContactBackup = DISTINCT(UNION(DISTINCT(YOUR_TABLE[Contact]), DISTINCT(YOUR_TABLE[Backup])))

Then create a measure with the following :

Selected Contact Or Backup = SELECTEDVALUE('DistinctContactBackup'[Contact])

After, create a measure with the following (like what Greg_Deckler told you):

Selector Contact Backup = IF( MAX(YOUR_TABLE[Contact]) = [Selected Contact Or Backup] || MAX(YOUR_TABLE[Backup]) = [Selected Contact Or Backup], 1, 0)

On your visual, add the measure and filter when the measure "Selector Contact Backup" = 1.

Add a segment with the values of your new table DistinctContactBackup.

Then you need to select the value you want.

Have a nice day.