class Program
{
  static void Main()
  {
    var cd = new ConcurrentDictionary<Foo, int>(new FooComparer());
    foreach (var f in new[]
    {
      new Foo(),
      new Foo(),
      new Foo{Bar = "A"},
      new Foo{Bar = "A"},
      new Foo{Zot = "B"},
      new Foo{Zot = "B"},
      new Foo{Bar="A", Zot = "B"},
      new Foo{Bar="A", Zot = "B"},
      new Foo{Bar="A", Zot = "C"}
    })
      Console.WriteLine("{0} : {1}", f, cd.TryAdd(f, 0));
  }
}

public struct Foo
{
  public string Bar;
  public string Zot;
  public override string ToString()
  {
    return $"Bar={(Bar ?? "null")}, Zot={(Zot ?? "null")}";
  }
}

public class FooComparer : IEqualityComparer<Foo>
{
  public bool Equals(Foo x, Foo y)
  {
    var f1 = (x.Bar == null && y.Bar == null) ||
         (x.Bar != null && y.Bar!=null && x.Bar.Equals(y.Bar, StringComparison.Ordinal));
    var f2 = (x.Zot == null && y.Zot == null) ||
         (x.Zot != null && y.Zot!=null && x.Zot.Equals(y.Zot, StringComparison.Ordinal));
    return f1 && f2;
  }

  public int GetHashCode(Foo foo)
  {
    var hashes = new[]
    {
      foo.Bar?.GetHashCode() ?? 0,
      foo.Zot?.GetHashCode() ?? 0
    };
    return hashes.Aggregate(hashes.Length, (current, t) => unchecked(current * 314159 + t));
  }
}

Bar=null, Zot=null : True
Bar=null, Zot=null : False
Bar=A, Zot=null : True
Bar=A, Zot=null : False
Bar=null, Zot=B : True
Bar=null, Zot=B : False
Bar=A, Zot=B : True
Bar=A, Zot=B : False
Bar=A, Zot=C : True