Why is filtering by custom country multi-select in a Drupal View not working?
Views is going to have a tough time handling this field, it generally likes a better table structure. I wouldn't call this a views handler problem, but an implementation problem - using the CiviCRM multi-valued custom field is just going to be problematic for views.

You could try getting views to create a different sql query with a LIKE instead of equal to the country id, but that'll be flaky.

I'd consider instead using a Drupal user field to store that value.