You can cross two arrays and then check to see if there are elements in it:
var stringArray1 = new string[] { "ABC", "EFG", "HIJ" };
var stringArray2 = new string[] { "123", "456", "ABC" };
var result = stringArray1.Intersect(stringArray2).Any();
, StringComparer Intersect. :
var result = stringArray1.Intersect(stringArray2, StringComparer.OrdinalIgnoreCase).Any();